Common flasher units are basically a bi-metallic switch. Electricity passes through the closed switch and the turn signal bulb lights up.
But that flow of electricity heats up the metal in the switch. One side then bends from the heat and a little set of points open. This cuts power to the bulb and the bulb goes off. The switch quickly cools and the cycle repeats itself... on, off, on, off.
Since you put a new flasher in and that seemed to help, maybe just disturbing the wiring in that area was what fixed the problem. Like you might have a stripped wire or a broken wire in there someplace. Or, a bad connection could have burned out that new switch.. (but check that flasher before assuming it is actually burned.. no point in wasting money on a new one if that one is still ok).
Examine the flasher's plug connector and all related wiring nearby. Use a multimeter (or ohm meter or continuity checker) and make sure the hot wires are never grounded to the frame, and that the turn signal ground wires certainly are grounded.