I'm assuming you have a Signal Stat 900 (or one of it's clones). Are the front turn signal lamps integrated into the parking lamp sockets or are they separately mounted on the fenders?
Rear brake/turn lamps use the same filaments, so wiring from the turn signal switch to the rear lamps are okay.
My guess is that the fuse between the "X" (see picture) terminal on the flasher and 12 volts is blown.
'57 GMC 102, Original 347 V8, HydraMatic, 3.08 rear gear, added A/C, disk front brakes, HEI, AFB carb, '98 Honda Black Currant paint. T-boned and totaled 10/12 '52 GMC 152 Stake Bed, Original 228, SM420, added A/C, HEI, disk front brakes, '67 Chev 3.55 rear gear. Gets used as a real truck.