1. The chicken will cool down over time. Slapping it fast enough to overcome this may or may not require much faster hand movement... so you'll need a lot of hands, and more slaps if they're not all at the same instant (which, seeing as the surface area of the chicken is not thousands of times the surface area of a hand, they
won't be at the same instant).
2. With a hand moving 3726 MPH, you might actually be able to generate a lot of heat from
aerodynamic heating, a.k.a. the reason spacecraft need heat shields for safe reentry. That's about Mach 5, and spacecraft fall at about Mach 20, so it probably won't incinerate the food, but it could actually lower the speed you'd need to send an invincible hand flying at your rotisserie chicken to cook it. And if you do cook it too hot, you might give yourself cancer, but if you can slap stuff at mach 5, you're probably invincible anyways, so who cares?
...PETA, probably. They probably care if you slap chickens at mach 5. But it's not like PETA would have the power to stop someone capable of mach 5 slaps.[
citation needed]