The flasher relay is not located in the relay box, and is not swappable with other system relays. Also, the turn signals do not flow through any of the relay box relays, so swapping them around won't do any good (I just pulled all my Firebolt relays to verify this and my signals still worked fine). The flasher relay is located behind your 9R front fairing, just above the low beam headlight.
If the flasher relay is bad, you can get a replacement from the dealer or use a cheaper generic 3-prong flasher relay from Autozone or your favorite car parts store. It should cost less than $10 and would be a relatively quick and easy swap to see if that's the problem.
If you have a wiring problem related to one of the blinkers, you might try isolating the offending blinker by disconnecting them from the system one at a time until the symptoms change.
If none of the above have any effect on the problem, then you might have a harness short somewhere like Stevenc150 mentioned. Look at the wiring in the front fork stem area where the harness passes from the fairing and instrument panel to the rest of the bike. Sometimes wiring gets pinched or rubbed through as the bars move left/right. You might get lucky and spot it. If you don't see anything obviously worn or shorted, try wiggling the harness wires around while the blinkers are malfunctioning to see if the symptoms change.