Why do they say choke the chicken?

(idiomatic, slang) Of a man: to masturbate.

What does choke the turkey mean?

By being interchangeable, choke tubes allow you to customize your shotgun to the type of hunting you'll be doing. “Chokes are designed to make it an all-around shotgun so you can use it as a bird gun, a target gun, a turkey gun, and make it effectively shoot the shotshell load you have,” Carlson said.