The chain can not backfire. If it is installed off time it can cause a backfire, which could conceivably damage a starter.
Incorrect Timing Can Cause Backfire.
Signs of a worn timing chain are difficulty starting in cold weather with backfire and sudden brief loss of power while accelerating or decelerating ("stumbling").
The starter turns the flywheel at the back of the engine. When the flywheel turns the whole engine turns. The timing chain is on the other end at the front of the engine. It is connected to the crankshaft and camshaft (s). So indirectly yes it does. If the whole engine is turned but the timing chain doesn't, there is a problem. Probably a broken timing chain.
Well it could be that your timing might be off if it didnt backfire before,i would get the timing checked or go back to where you got it done.
A back fire is usually the result of an engine timing issue between the cam and the crankshaft. If the mileage is high and it uses a timing chain, you may need to change the chain, gears, cam. IF it uses a timing belt, change the belt.
Incorrect timing, spark plug wires not installed correctly, timing chain worn out and has jumped a tooth, or distributor worn out.
Car will run rough ,backfire and you may be able to here it rattling.
The ignition timing is not set correctly or the timing chain is worn out or installed incorrectly.
there is a few things that could be wrong, its very possible that the timing chain is shot or the crank positioning sensor is bad
timing chain or distributer --or gypsies, gremlins etc.......
Not sure what engine you have but it is highly unlikely the timing would jump being that it is driven by a chain. If it was to jump it probably wouldn't start and possibly backfire in the attempt to start.
It will buck, choke & backfire but as long as you don't persist (shut it off right away) it should be o/k. Set the timing properly (15BTDC), firing order is 142536, # 1 cylinder is passenger rear. On any engine, the possibilities are, break a timing chain, bent a rod, backfire.