Does the hazards work? And do you hear the flashers blinking from the dash? If the hazards work, then I would tend to think that the EFM (Electronic Flasher Module)is going bad. It is located left side of the stereo behind the center console and under the steering column. If it is original, never replaced, it should be yellow, and square 1" by 1" relay module. If a plug and play relay, costs about 5 bucks at a local auto parts store. If that is working and not bad, then the only other area of concern would be the multi-function switch which is the turn signal lever that attaches tot he steering column and has 3 plugs going into it.
But check the EFM first.
2015 Race Red Performance Package GT 5.0 (435hp) stock
Still in the making Updates coming soon!