Can Konohamaru summon the Monkey King Enma? Has it been revealed what Konohamaru's summons is? Did he inherit his grandfather's summons or did he show an affinity for frogs?
Can Konohamaru summon the Monkey King Enma?

Maybe. We can't be sure until we see it.

Has it been revealed what Konohamaru's summons is?

No.

Did he inherit his grandfather's summons or did he show an affinity for frogs?

We can assume none of them for now. Same as Asuma Sarutobi who didn't summon Enma or any other summoning animal either. 



If I still have to make a wild bet then I will assume it's frog as Konohamaru is more of Naruto's follower and never seen trying to do any of his grandfather's Jutsu. And remember his grandfather was not around to pass on the contract to him and we never see any other Monkey King summoner who can teach him that but Naruto is still there.



In Boruto: Naruto Next Generations episode 4, we see he can summon toads and he summons Gamagorō.