While positioning your fingers on the flute, there is one key left out between the left hand 2nd and 3rd finger. I’ve noticed that it does the same thing as the Bb Thumb Key. I prefer to use it while trilling between Bb and B, and in pieces like “Radetzky March”, where the notes after the Bb and the B are below it. It there any downside to doing so? I can change the 3rd finger to the A key relatively fast.
This is a classic example of "Get thee to a teacher." The flute family, like the clarinet family, sax family, and AFAIK the double reeds, have many alternate fingerings available by design. Which fingering to use depends on the passage as a whole: what fingerings must be used before and after the note in question, and what minimizes finger motion? It's always best (until you become a semi-pro quality player) to discuss fingering patterns with an experienced teacher.
As a point of possible interest: clarinets in particular have keys set up so that several notes (bottom of each range) can be played with either little finger; once in a while a passage comes along which requires one to use first one finger, then "transfer" to the other little finger within a single note!
Don't see any downside if it's comfortable for you, and doesn't get you confused. The standard fingerings for Bb are of course going to be better for fast scale passages, etc.
I think this is not a good choice. With flute, your grip on the instrument is already a bit tenuous, and shifting the hand to play it in a nonstandard way could cause problems. Why not just use the normal T1--|1-- fingering?