You did use a 6v flasher unit, yes? 6v bulbs draw more current than 12v bulbs and if used with a 12v flasher the heater element (bi-metal) in the 12v flasher might be heating up and flicking off/on too rapidly. That's my first guess. Even if the flasher you bought is marked as 6v, it might have been made in a 5-letter country beginning with the letters CH which isn't CHILE. Look at the embarrassingly dismal job they've done with a simple product like automobile condensers.
The fog lights might be part of the problem. Small chance they don't draw enough current to cause the flasher to work right. If the flasher sees a burned out bulb, it goes wonky. Not to bore, but there's a bi-metal strip and contact points in there. As it is activated in the circuit, resistance causes it to heat. One side of it bows in more than the other side and that causes it to go arc-shaped and pull the points apart. That's all that's happening in there, but it must be the proper flasher for the current (amperage) pulling through it.
Just an outside thought, but was there any chance these were LED bulbs? Maybe 2 of them were LED bulbs? Vintage type flasher units can see those as being burned out (since their current usage is much lower) and this can cause erratic flashing. If you're using a 6v flasher and this problem started from day one and the lights never blinked correctly before that certain point, it hints there is a bulb problem...but honestly it seems to me kind of a stretch unless it emanates from your fog lights. What I mean is if both right and left side are blinking rapidly, then there has to be a lack of connection or bulb problem on both sides. If the wiring is new, the bulbs are correct for the sockets and the flasher rating and the sockets are good and clean, the coincidence factor drops a lot. One bulb on one side might be failing to connect, but two is a stretch.
And the dead horse has been beaten here quite a lot, but ground connection is very important. An intermittent ground connection will cause this, but you may not have brightness when that's happening. An intermittent ground connection normally will cause a bulb to flicker dimly and then maybe catch and burn ok for a bit and then go dim again.
One more idea...and this is a thought from distant past...was it a heavy duty flasher? A friend in high school had this happen and it turned out the heavy duty flasher was the problem. As I recall with only 2 bulbs per side it didn't get enough current draw to flash right. If you suspect this, you could connect an extra bulb (or two) to both sides of the wiring (left and right) and see what happens. Or...if your flasher has the option of hazard lights, flash all 4 at once. That might provide enough current for you. Good luck.
