[Dead Parrot]

Possible something is putting static into the electrical system with the motor running. The old style bi-metal flasher didn't care about static but the new electronic ones are probably more sensitive.

Check that you don't have a plug wire close to another wire.
Make sure all the battery and alternator connections are tight and cables good.
As others mentioned, check your voltage. Possible the voltage regulator is bad and your alt is putting out too much voltage.