Marvel openly says that Johhny covers his body with flames when he "flames on." He doesn't become a giant ball of flame. His body is still under the fire.
If he became fire itself, it would be fair to say that the fire's consumption of oxygen is equivalent to his own; for him burning oxygen equates to breathing.
Since he is still alive when he flames on, he needs to breahte in order to stay conscious. There are multiple incidents (in movies) of him losing conscious when he couldn't breathe and him losing his flames.
In comics, there was one moment when he could not flame on because of his inner doubts, and is a metaphor for his wasted potential. But this had nothing to do with breathing.
And in "THE FALL OF THE FANTASTIC FOUR" PART 4, Johnny loses his powers but I haven't read the issue so I'm avoiding spoilers. I highly doubt it is oxygen-related.
Human Tourch needs to breathe. But the kind of oxygen consumption you are referring does not entirely work when you consider how much he breathes at a time and how much his lips could burn.