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check the carberauter
The best answer for this is: Get a tune-up.
If it is backfiring the timing is set incorrectly or the spark plug wires are not connected in the correct order.
The engine backfiring at idle, and at slightly off idle speeds is indicative of a lean fuel/air mixture. Try enriching your fuel mixture.
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Poor upkeep try cleanig the airfilter if that doesent work try cleaning out the carburetor I have a yamaha 350 bruin I had the same problem
There are a few online resources that offer information about the Yamaha FJR 1300, including Motorcycle News, Gogo Cycles, Rider Magazine, Web Bike World, and The Old Bloke.
On the engine, stamped somewhere on the cases
Check the reed valves 1 is probley broken if it is baackfiring thru the carburetor.
it is either your fuel lines arnt hooked up to the carbarator right or your fuel lines a clogged and it is starving for gas
Rev the engine six or seven times before coming to a complete stop. Rev it all the way to the edge every time you stop.
To bleed the cluth on a Yamaha Royal Star 1300 first drain all of the brake fluid from the vehicle. After draining the brake fluid pump the brake pedal up and down several times. All oil will then drain from the system.