So Master Yoda teams up with Luke Skywalker-CotF. Can Luke Use the Force to Crit, then flurry, then get the Yoda extra attack, or would he have to take his normal attack, then use the force on Yoda's CE, then Flurry.

Also if he rolls a natural crit, how does the interaction work.

He only gets the CE if he has only made one attack at the end of his turn. Natural 20 means Flurry triggers and thus CE does not come into effect.

But as the op mentions, I believe you can make your normal attack and assuming it is not a crit you then can make an attack via Yoda's CE and spend the FP then for Use the Force making that attack a crit and thereby triggering a flurry attack. Same result, just a matter of the order in which you declare things. Someone can correct me if I'm wrong but I believe that's the way it works.

And if you happen to roll a natural 20 on the initial attack triggering flurry and then spend the FP to us the force triggering another flurry then you are going to be in good shape even w/o getting to use Yoda's CE.