There's a thread posted in here titled "Jeep is Ill", which describes kinda the same problem I had this week.
I would put my left flasher on and the dash light and fog lights would flash on and off.
It turned out to be the flasher socket which was all corroded inside, causing a short.
I suggest you look at each one of the flashers, starting with the front. Just reach up under the fenders and turn the socket 90°...it should come out. Pull out the lightbulb and check the four little wire contacts, if they're screwed up, then that's your problem. If not, check out the contacts in the socket for crud. Do the other front flasher and the back ones too. If you have any doubts about the bulbs, change 'em....they're cheap.
Let us know how it works out.
2000 TJ...Almost stock
Quick Discos and MT/R's.