Presumably the combusion is a result of other particles in the air oxidizes around the Human Torch. Wikipedia says this about combustion
In reality, as actual combustion reactions come to equilibrium, a wide variety of major and minor species will be present such as carbon monoxide and pure carbon (soot or ash). Additionally, any combustion in atmospheric air, which is 78% nitrogen, will also create several forms of nitrogen oxides.
When you place a jar over a candle and it goes out, it isn't necessarily because all of the oxygen is gone. From a candle experiment:
Take a large jar, (a desiccator will do well), fix a tall candle in the bottom and put a mouse in the jar (Figure 2). Light the candle and seal the jar. The mouse will NOT die. In fact it will probably not even be a bit distressed. The candle will, however, go out in the usual way. Clearly there must be a fairly minimal gas change in the atmosphere. (Actually, the candle probably "drowns" in the hot CO2 in the top of the jar, which the mouse is too low down to experience.)
It is likely that the Human Torch would stop physically burning before all of the oxygen is consumed. The CO2 (or nitrogen oxides as it were) would eventually cause little enough oxygen to be present around him to cause him to be extinquished.
In a small enough space with a fast enough fire (such as a small room in which 100% of the surface area was on fire) the oxygen COULD be completely consumed, or consumed at such a rate that there would be suffocation.
Thanks to @JohnRennie for working out some math for the Human Torch oxygen consumed part.
He speculated that the Human Torch burns anywhere between 1.1 x 10 −6 moles or 3.6 x 10 −5 grams of oxygen per cm^2 per second and 340 moles or 10.9kg of oxygen per second or about 0.55g per cm^2 per second. This is depending on total energy output (or heat) he is deciding to produce.