Considering that Kirby and Yoshi's methods of eating things typically require fully engulfing the thing in their mouth all at once (Exceptions: Cloud N. Candy; probably also some Kirby bosses I don't know about), they can't logically eat each other at the same time. The closest they could get would be French kissing.
What would happen if they both tried to eat each other at the same time? In a standard matchup, a full-grown Yoshi would win, as Kirby is only 8 inches tall. If we were to cheat and go with the relative scales in the Smash Bros universe, I think Kirby would have the advantage. For Yoshi to win, he needs his tongue to make contact with Kirby's body so the tongue can adhere to him and pull him in. Starting at the same time, Kirby would probably be able to suck Yoshi's tongue into his mouth and swallow it before it hit his body. However, as long as we're cheating, a super-happy Yoshi would have a much longer and faster tongue, which may turn things back in his favor. Depends on how far apart they are.