Reading a few of Klines other articles, I think I've misinterpreted his angle upon common grace. The below linked articles and excerpts reveal that Kline's concern about common grace is related to his views on the Noahic covenant and the abrogation of that covenant at the last day. He argues contra both pre-millenialism and post-millennialism that there cannot exist a kingdom that enjoys blessings on the basis of messianic promises and covenantal faith until the Noahic covenant of common grace is abrogated.
"The world order of common grace is covenantally formalized in the post-diluvian revelation to Noah (Gen. 8:15-9:17). This covenant of God with all the earth granted to the just and the unjust in common a measure of the blessings of earthly life, including the provision of the judicial structure of the state. And God defined this arrangement as one that would continue valid and operative until the termination of the present cosmos. The consummation will introduce through cosmic re-creation a world order in which no blessings of any kind are apportioned as a common gift in which the unjust participate but all blessings are for the beneficiaries of special redemptive grace alone. Until that re-creation, however, the order of common grace is firmly established by divine stipulation and decree. It is open to penetration at points by the world order to come, but it is not subject to eclipse until the consummation.
The millennium envisaged by classical premillennialism is in conflict with the terms of the covenant of common grace. It features a theocracy on earth before the consummation, a universal kingdom of Christ in which those blessings hitherto received in common by all men and often in greater measure by the unjust than the just are no longer apportioned according to the principle of common grace but according to a policy of special favor to the people of God. The redeemed are in fact already in possession of glorified natures and experience their public vindication over against the world of unjust men. The premillenarian’s millennium would thus abrogate the common grace order prior to the consummation, in contradiction of God’s covenantal guarantees."
and
"Along with the hermeneutical deficiencies of Chalcedon’s [Chalcedon Foundation?] postmillennialism there is a fundamental theological problem that besets it. And here we come around again to Chalcedon’s confounding the biblical concepts of the holy and the common. As we have seen, Chalcedon’s brand of postmillennialism envisages as the climax of the millennium something more than a high degree of success in the church’s evangelistic mission to the world. An additional millennial prospect (one they particularly relish) is that of a material prosperity and a world-wide eminence and dominance of Christ’s established kingdom on earth, with a divinely enforced submission of the nations of the world to the government of the Christocracy. For example, appealing to Isaiah 60:3, 10, 12, Bahnsen declares that during the millennial period the kings of the Gentiles will either minister unto God’s kingdom or they will utterly perish (p, 428).
The insuperable theological objection to any and every such chiliastic construction is that it entails the assumption of a premature eclipse of the order of common grace. [10] That order was formalized in the post-diluvian world by the divine covenant of Genesis 9 and by the terms of that covenant it is in force as long as the earth endures, that is, until the cosmic re-creation at the consummation (cf. 2 Pet, 3: 7, 11-13). A basic and essential structure of that common grace order is the institution of the common state. This civil institution, unlike the nation Israel, which was separated unto a distinctive institutional identity as a holy, redemptive, theocratic kingdom, is not a holy but rather common institution, with its citizenry a mixture of both the holy and the non-holy. It does not, as did the Israelite kingdom, possess special guarantees of a material prosperity unfailingly equal to the measure of its obedience to the law of God nor does it enjoy the promise of an ultimate perfecting of its beatitude. Its prospect is that of eventual termination rather than consummation. And meanwhile it must run its course within the uncertainties of the mutually conditioning principles of common grace and common curse, prosperity and adversity being experienced in a manner largely unpredictable because of the inscrutable sovereignty of the divine will that dispenses them in mysterious wisdom."
The First Resurrection: A Reaffirmation - Meredith G. Kline Resource Site
Meredith G. Kline, “The First Resurrection: a Reaffirmation”
meredithkline.com
"The world order of common grace is covenantally formalized in the post-diluvian revelation to Noah (Gen. 8:15-9:17). This covenant of God with all the earth granted to the just and the unjust in common a measure of the blessings of earthly life, including the provision of the judicial structure of the state. And God defined this arrangement as one that would continue valid and operative until the termination of the present cosmos. The consummation will introduce through cosmic re-creation a world order in which no blessings of any kind are apportioned as a common gift in which the unjust participate but all blessings are for the beneficiaries of special redemptive grace alone. Until that re-creation, however, the order of common grace is firmly established by divine stipulation and decree. It is open to penetration at points by the world order to come, but it is not subject to eclipse until the consummation.
The millennium envisaged by classical premillennialism is in conflict with the terms of the covenant of common grace. It features a theocracy on earth before the consummation, a universal kingdom of Christ in which those blessings hitherto received in common by all men and often in greater measure by the unjust than the just are no longer apportioned according to the principle of common grace but according to a policy of special favor to the people of God. The redeemed are in fact already in possession of glorified natures and experience their public vindication over against the world of unjust men. The premillenarian’s millennium would thus abrogate the common grace order prior to the consummation, in contradiction of God’s covenantal guarantees."
and
Comments on an Old-New Error - Meredith G. Kline Resource Site
Meredith G. Kline, “Comments on an Old-New Error”
meredithkline.com
"Along with the hermeneutical deficiencies of Chalcedon’s [Chalcedon Foundation?] postmillennialism there is a fundamental theological problem that besets it. And here we come around again to Chalcedon’s confounding the biblical concepts of the holy and the common. As we have seen, Chalcedon’s brand of postmillennialism envisages as the climax of the millennium something more than a high degree of success in the church’s evangelistic mission to the world. An additional millennial prospect (one they particularly relish) is that of a material prosperity and a world-wide eminence and dominance of Christ’s established kingdom on earth, with a divinely enforced submission of the nations of the world to the government of the Christocracy. For example, appealing to Isaiah 60:3, 10, 12, Bahnsen declares that during the millennial period the kings of the Gentiles will either minister unto God’s kingdom or they will utterly perish (p, 428).
The insuperable theological objection to any and every such chiliastic construction is that it entails the assumption of a premature eclipse of the order of common grace. [10] That order was formalized in the post-diluvian world by the divine covenant of Genesis 9 and by the terms of that covenant it is in force as long as the earth endures, that is, until the cosmic re-creation at the consummation (cf. 2 Pet, 3: 7, 11-13). A basic and essential structure of that common grace order is the institution of the common state. This civil institution, unlike the nation Israel, which was separated unto a distinctive institutional identity as a holy, redemptive, theocratic kingdom, is not a holy but rather common institution, with its citizenry a mixture of both the holy and the non-holy. It does not, as did the Israelite kingdom, possess special guarantees of a material prosperity unfailingly equal to the measure of its obedience to the law of God nor does it enjoy the promise of an ultimate perfecting of its beatitude. Its prospect is that of eventual termination rather than consummation. And meanwhile it must run its course within the uncertainties of the mutually conditioning principles of common grace and common curse, prosperity and adversity being experienced in a manner largely unpredictable because of the inscrutable sovereignty of the divine will that dispenses them in mysterious wisdom."