What is the mechanism of alkane combustion?
The following, very general radical reactions apply to any common combustion reaction of organic material. Details vary largely.

Step 1

An energy spark of whatever kind turns triplet oxygen into its high energy singlet state$^*$, which typically strips a hydrogen atom off of some organic molecule
$\ce{R-CH3 + O2^* -&gt; R-CH2. + HOO.}$
Now you have two radicals.

Step 2

The perhydroxy radical strips another hydrogen off somewhere,
$\ce{R-CH3 + .OOH -&gt; R-CH2. + HOOH}$
while the alkyl radicals react with more oxygen (self-catalysed)
$\ce{R-CH2. + O2 -&gt; R-CH2-OO.}$
$\ce{R-CH3 + .OO-CH2-R -&gt; R-CH2. + HOO-CH2-R}$
, this incorporates $\ce{-OOH}$ hydroperoxide motives into more and more molecules. This is in itself a linear process, with a constant number of radicals. Very similar to free-radical polymerisation or organic radical-substitution reactions, and very much the same as formation of the infamous ether hydroperoxides.

Step 3

These peroxides are not stable at elevated temperature, and their O-O bond tends to split homolytically
$\ce{R-OO-H -&gt; R-O. + .OH}$
Now the number of radicals grows rapidly, the combustion is gaining speed.

Step 4

As temperatures rise (see step 5!), esp. larger organic molecules start to break up also by themselves
$\ce{R-CH2-CH2-R -&gt; R-CH2. + .H2C-R}$
(That's also a possible initiation step.) You get more radicals, which can react with more oxygen to form peroxides. Now the chain reaction snowballs!

Step 5

$\ce{HOOH -&gt; HO. + .OH}$ gives more hydroxy radicals (also from step 3), which turn into water
$\ce{HO. + H3C-R -&gt; H2O + .H2C-R}$
leaving another radical behind. Producing water is highly exothermic, this fuels the reactions creating radicals (in steps 3+4+5). Making radicals costs a lot of energy.
Steps 2-5 (it's really not a sequence) run in parallel and repeat as they produce more radicals and peroxides all the time. The reaction is usually limited by the inflow of fresh oxygen.

Step 6

Termination: Two carbon radicals can recombine, but at high temperature this does not really happen, because the energy from the recombination has to go somewhere. When temperatures are too low, this makes coke and smoke.
This picture is by no means complete. $\ce{CO2}$ would likely occur via decarboxylisation of $\ce{R-COO.}$ radicals, etc.  Organic radicals at high temperatures have more internal reactions where they split off smaller molecules, e.g. $\ce{R-CH2-CH2. -&gt; R. + H2C=CH2}$. (The latter can be seen as depolymerisation of polyethylene.) A radical in the middle of a chain splits it in half ($\ce{R-CH2-CH2.-R -&gt; R. + H2C=CHR}$, increasing the volatility.
And remember that this picture is terribly simplified. I'm by no means an expert on this subject, and the experts also have not agreed on all details yet, especially since it varies a lot.