First thing to check would be the fuse that controls the turn signals.
After you verify a good fuse, see if the flasher is getting power when the switch on the handlebar is engaged. If no power to the flasher, I would suspect a bad handlebar switch or faulty wiring in the circuit from the battery to the switch to the flasher. The constant flexing of the wires as the handlebars are turned back and forth can lead to an internal break in the wires.
I assume your bike has running lights in the front turn signals like my KZ1100 does. Do the running lights come on when the ignition key is turned on? If so, then you know you have power to the signals.
Have you confirmed that the new flasher works? VERY CAREFULLY put 12 volts to it using the bike battery, a car battery, a battery charger, etc., and see if it clicks. Depending on the type of flasher you bought, you might also try putting it into a car with known working turn signals.
T.J. in Huntsville, Alabama
1983 KZ1100-A3, 1974 Honda CB550-4
Previous bikes: CB100, TS125, CB175, KZ400, CB500-4