I'm sorry but I don't believe that is correct. The visible part of a flame is impurities in the air igniting, but flame itself does not necessarily emit any visible light. Hmmm, this is a little complicated...
I found this thread looking to verify what I had said to a classmate earlier today, namely that fire is indeed a plasma.
The visible light emitted by a fire is impurities being burnt within the intense heat caused by fire. That said, pure natural gas burns without emitting any visible light...