Pretty close to zero. His dissertation ("Belgian education policy in the Congo 1945-1960," 1971, Tulane) does not show up as a citation in anything I've read on social policy in colonial Africa. That may be because he dealt with Belgian colonial education in Central Africa without ever bothering to go beyond Brussels. As dissertations researched in the late 1960s go, it wasn't great, but it wasn't awful; a lot of colonial histories never engaged with the colonized at that point. However, it wasn't a truly finished study and it never became a book, whether or not he attempted to submit it to a publisher (which we do not know). He produced no essays from it, and no journal articles, and I see no book reviews by him between 1970 and 1978 on the indices I have access to. I'm not sure if he presented at professional conferences, but I see no evidence there, either. He was ambitious and full of ideas for his new institution, as the WSJ noted in 2012--and he hopped disciplines, made plays for headships, and reputedly even the presidency of the institution--but ultimately that ambition did not serve his original academic path or build influence there. [If I'm wrong and somehow missed a 1970-78 pub, please let me know.]

Wikipedia glaringly omits the very relevant point that he was denied tenure at West Georgia because he produced no published works at all, and instead characterizes it as totally his choice to depart when he was elected to office. Professionally, that's a pretty major difference, and one that speaks further to his null influence among historians in his original speciality. Of course, he espouses different historical specialities now centered on the US, and his influence on those points in the public mind--whether or not one agrees with his views--is far, far greater. But in the subject area of his PhD or those immediately adjacent, his work has no pull, and I don't think he's ever tried to position himself to have any there. I've only seen two or three citations of the thesis that aren't making an unrelated point or covering readings of his work as a means of scrying for his internal beliefs about force projection, race, etc. in recent Presidential election cycles.

That much of his failure to publish at West Georgia probably stemmed from his shift to politics, and that his successful run came five or six months after his tenure denial, are beside the point regarding his influence in the study of colonialism (African or more generally), Belgian/European colonial rule, or education policy therein. Certainly he has no ongoing influence on scholarship on Africa proper as a historian, although anyone working on education in Congo would be remiss not to cite and possibly address his work in a standard lit review because so few like it exist, flawed or not. [edit: Gingrich's shift in occupation and interests of course do not invalidate his training, his display of mastery of the relevant skills by earning a PhD, or his consequent right to claim his qualification as a historian, formal post or not.]

(Incidentally, the Newton Gingrich who wrote a short book on the history of the Ontario Mennonite Bible School around 1971 is a totally different person--Rev. N. L. Gingrich--who died in 1979.)