If it's the same as an '06, and if I remember correctly (not at home right now with my wiring diagrams), that circuit is fuse, flasher relay, switch, and then to lamps. Would have to be one of those or a broken wire or bad connector/ground connection somewhere in the circuit. Not likely to be inside a wiring harness. Also not likely, but within the realm of possibility that all the turn lamps are bad.
2006 Vulcan 500 LTD
2013 Suzuki V-Strom 650 ABS Adventure