ken-ichi said:How do you get invisible flames that emit light from a continual flame spell?
Umm... magic

You are thinking of it from a physics point of view, it is comeing from a magic point of view.
If you want to take it that far then creatures who are invisible should be blind as well. After all, the photons are passing right through you (or bending around you depending on the way flavor text of the setting) and so are not being absorbed by the photo receptors in your eyes. No photons to the rods and/or cones? no sight.
But of course I still put it with, 'if your dm does this' because if you look at the invisiblity spell itself it says that the object emitting the light becomes invisible but the light itself never does. One could read this in a couple of different ways but the least likely one is the one that my last dm picked.
It was a fun way to do it. Completely nonsensical to me with my physics degree, but completely reasonable within the bounds of 'its magical, and hey you can see while invis so shut up physics'
