I thought the Felix Felicis was empty after Ron, Hermione and Ginny used it in HBP.

I don’t know.

I mean u know right.. He gained the potion in his 6th year.. He already know and plan to kill Riddle. So why not use it? It's worth to try i think

Yeah. But after a while, Felix isn’t effective anymore and Harry would constantly drink this. Which would kill him after a while. I think something like that says Slughorn.