Dash lights blink with left turn signal

Backfeeding through the circuit & w/ headlamps on the hot wire is taking away that ground. In other words you've got an interruption in the ground side & it's finding it's way back through the circuit & then with the headlights on the positive side of the circuit now energized takes away that path to ground. You can't have 2 positives in a circuit.
Also look for incorrect bulbs in your turn signals & tail lamps.(Like a single filament bulb in a double filament socket)