I've been flyfishing from kayaks for several years and love it. A recreational kayak is good and stable. Mine is an Old Town Loon 138, nearly 14' long and stable as a rock. Mostly I fish lakes and the Susquehanna River.

Touring kayaks are faster, but less stable for fishing. Whitewater kayaks are as stable as a two-legged chihuahua on crack, and have no use for flyfishing.