Charizard cannot learn Flamethrower by a normal charged TM.
In Pokemon Go, Elite TMs don't just give you the list of moves to choose from, it also allows you teach your Pokemon exclusive moves that cannot be learnt by plain-old regular TMs. These moves can be Raid Legacy moves which the Pokemon has in Raid battles or Community day moves. For example, you can get Air Slash as fast attack with a normal fast TM, but if you want to get Ember, you need to use an Elite fast TM.
So, to get Flamethrower, one must use an Elite charged TM. You can get Elite TM by purchasing them from shop for money or get them from Timed researches. While that is how you get Flamethrower, it doesn't mean you should. Blast Burn is another one of Charizard's charged attack, and is far better; taking the same amount energy but doing much more damage. You get Blast Burn the same way you get Flamethrower; by using an Elite charged TM.
When you use the TM, both Blast Burn and Flamethrower will be on top. And while I heavily suggest using Blast Burn, which move to choose is up to you.
Hope it helped!