The Collaborative International Dictionary of English v.0.48:
Fleshy \Flesh"y\, a. [Compar. Fleshier; superl. Fleshiest.] 1. Full of, or composed of, flesh; plump; corpulent; fat; gross. [1913 Webster] The sole of his foot is fleshy. --Ray. [1913 Webster] 2. Human. [Obs.] "Fleshy tabernacle." --Milton. [1913 Webster] 3. (Bot.) Composed of firm pulp; succulent; as, the houseleek, cactus, and agave are fleshy plants. [1913 Webster]