Have you even seen how many Flappys there are on Scirra Arcade posted every day ? You know, actually the guy who made flappy bird, the popular one, got accused by local (viatnamese) newspapers that he cloned the idea from another game called Piou Piou vs. Cactus which was released 2 years prior. Source: Wiki
In your case, right here? Free, I mean non-commerilized, no-ads flappy bird game? I dont see any way you getting in trouble making another one.