So far, the 3 moves you planned out so far are both fire and dragon types. In result, it's super-effective against 5 types. Flare Blitz is a strong move, but results in recoil - good for the max attack though. However, Fire Blast is also a strong move, but it has only 85 accuracy - and also goes under your special attack (the weaker side). I think you should have only 1 fire move, and make it either fire punch or flamethrower (something certain and appropriate). Having 2 fire is your choice, but I would recommend taking one of these moves ; unless you prefer to be a rough fighter. Therefore, take 1 fire move and make it flare blitz. This is STAB #1.
STAB #2, dragon claw. Good move, no questions here.
If you take my suggestion - and have two empty slots left - I think you should substitute it with a dark, flying, or electric type move. Each of these types can provide you with 2 extra super-effective type coverage. Plus, charizard can learn good moves in each category: Crunch, Wing Attack, and Thunder Punch. The only downfall is the weaker flying type move. So, I suggest going with Thunder Punch and Crunch. Wing attack can hit all Pokemon in triple battle - if you find this useful. (these moves are tutor/egg moves)
Now, having a fire, dragon, dark, and electric type moves can provide 9 super-effective and neutral to the other types. If you want to keep 2 fire moves, take either electric or dark (2 extra super-effective). This would provide you with more PP and a biggest STAB move set.
Your Choice! Hope I helped! :)
