JFK COE in Heber Springs is a great campground right below the dam. It is right on the river and offers Great fishing for trout.
How the river is for a Kayak i do not know. So can't help there.
I do know as someone else already mentioned the Buffalo River is the place for Kayak and Canoe trips.
I made the trip down the river once many years ago in a canoe from one of the many outfitters in the area.
I have been to many of the State Parks in Arkansas and have not found a bad one yet. So those would be an option for you also.