One thing I enjoy about Falcon is that he usually has a better time recovering in doubles, recovering super high doesn't get punished as hard so use that to your advantage. Just keep doing upBs until your teammate comes to help you out.
Falcon's really fast so I try to take advantage of that. If your opponent stop applying pressure on you, it sometimes is better to ignore them and focus on 2v1ing the other with your teammate. It's a great way to force them to approach. That applies to doubles in general, but Falcon can be and needs to be very good at switching between his opponents to utilize his speed effectively.
I think Falcon is best staying on stage for the most part in doubles, as he can still get gimped offstage easily. My main teammate is a Sheik player, so I let him edgeguard the opponents from the ledge, and I focus on punishing them for landing on stage. It works out pretty well. It's something you have to feel out though, if your edgeguards are on point then definitely go for it, but if you don't think you can edgeguard an opponent, just let him take his time recovering and work that 2v1 with your teammate. That's especially important against floaty characters like Luigi and Samus, who take 20 years to recover. There's no point just waiting for them to come back (or going offstage and whiffing lol), just keep hitting them back off stage and work the 2v1.
Also work on grab combos. Falcon's good at this, if your teammate grabs your opponent, that's a free knee if you're quick enough. Just make sure not to knee your teammate too
