musictheory.net provides the ability to make custom web exercises to practice music theory topics. I have created several buttons below for custom exercises for FLUTE players. Please be aware that you will need these exact links to get the exact exercises you need.
I recommend that flute players not only try another size of flute, but also consider learning the basics of saxophone and/or clarinet. In pit orchestras and jazz bands, flute players are sometimes required to switch back and forth between multiple instruments. I have been selected for paying gigs because of my ability to play more than just flute.
After learning saxophone and clarinet, it is OK to learn double reeds like oboe and bassoon, but those are only necessary in some pit orchestras. I do not play oboe or bassoon because they are only very rarely used in jazz. Unless you are asked to learn a double reed for a concert band, I would recommend learning saxophone and clarinet first.
Flute is one of my weaker instruments, and I struggle with my embouchure regularly because I do not practice as often as I should. When I do not play for a while, there is a 50% chance that the next time I play that my tone isn't good.
I find that if I am struggling with my tone, usually the reason is because I have too wide of an airstream (probably from playing saxophone and clarinet). Once I close of my mouth more, I find that the tone tightens up and becomes much less airy in a good way. I also have to tweak the angle of my flute to find the sweet spot, or the spot that gives me the most flexibility for range and dynamics.
You physically cannot take enough air in on your inhales to properly play fortissimo flute for more than a few bars. It's just hard, but you can improve! I've heard a band director say something like "it takes more air to play a flute than a tuba" before I became a flute player, but now that I am a flute player, I believe that statement wholeheartedly. Have no fear, take giant breaths!