I have a cloth simulation. I have a manta-flow gas simulation -- "quick smoke" with the cloth mesh as the inflow object.
The flames do not follow the collapsing fabric (the goal), despite having pre-baked the cloth simulation. Instead, the cloth "falls out of" the flames, which continue to burn in the "old location".
I have tried several things, including checking the "initial velocity" checkbox in the domain settings.
The answer today is unfortunately the same as in 2011. They don't play together. People can do tricks to simulate cross-effects. I leave you with the following example 
where the Gas Inflow on the left is Shrink-wrapped to a Cloth (identical object with same number of vertices, Inflow was scaled to be a percent larger prior to the shrinkwrap). Compare this to the Cloth PLUS Inflow object on the right, where smoke appears to emit from the undeformed Cube.
This technique may or may not work in your case, as in my trivial case the cloth is probably well behaved, so that the shrink-wrap and cloth appear the same after simulation.
