What year/make is the vehicle? Something is suspect here. If the blinkers in the rear won't work, then the ones up front won't work either because there won't be enough load on the system to cause the flasher to work. What I think, is that you probably have one of your 1157 bulbs put in wrong and it is screwing up the system in the back. In fact, if you hit the brakes, I bet the front driving lights are illuminating. Get somebody to watch.
First, check all fuses. Then see if you are getting power to the bulbs. Then the next possibility would be the turn signal switch.
Answerpull the bulbs on the left and make sure they are not in with the tits in the wrong position. That is lower teet in the upper slot of the socket.
Check the switch on the brake pedal
fuse, bulbs
brake light switch would be most common cause
BAD BRAKE LIGHT SWITCH AT TOP OF BRAKE PEDAL
Possible ground issue at the taillights.
The BOO (Brake On/Off) Switch may need to be replaced. If it is bad, it would cause the brake lights to NOT illuminate when the brake pedal is applied.
Blown fuse or defective brake light switch.
Most likely a fuse.
The most probable cause is that the brake light switch is out of adjustment.
Check your brake light switch at hte brake pedal.