Basically, if you're fighting Falco, you want to get a good lead (30-50%) and just stay away from him. On a stage like FD, you really just need to duck and be on the look out for his super fast moves, of course, he has to approach first. If he approaches with phantasm, you should laugh at him, because from the length you're out, you should be able to punish this well. And now to be more serious, this isn't gonna happen. DTilt is the best move to use against approaches (in my opinion) as it's speedy, covers the air a bit, and is very deceiving. UpB in this scenario is godsend because it's also fast and gets you out of a situation very quickly. If the stage has platforms, you want to stay on top and use a mix up of slow Dairs and fast Dairs and retreating bairs. Also, empty jumps help out as well.
Avoiding the chain grab in the beginning is a part of the whole, 'chill out' part of this MU. Remember, UpB is one of the best ways to avoid being grabbed, and should be mashed while being chain grab just in case you get lucky (don't count on this)
Basically, winning this matchup is pure patience and little to no fighting, which is preeeetty boring.
Also, on the YI note, no I'm not saying it's the greatest starter, but it's definitely not Falco friendly, moreso than it is for us.