Yes, it should affect all flames within range
As you point out, the spells says "flames", not "a flame", or even "flames you choose". So, by a strict reading, all flames within the area of the spell (30 ft), would all adopt whatever effect you would choose to give them.
That being said, I would and have as a DM allowed players to more finely tune this spell effect to certain flames and don't force it to affect all of them by default. This has caused no issues and seems much more in the spirit of the spell as I read it (given that all the effects of thaumaturgy are very loosely written seemingly to allow for creative, but harmless, uses).
Either way, it clearly can affect the multiple flames in the area.