If driver a tells driver b that it is ok to turn left in front of driver a and driver b subsequently hits an oncoming driver c in the lane next to driver a is driver a liable for damages to driver c?

Left-turning vehicles are almost always liable for collisions with oncoming traffic.

It is unlikely that driver C or driver B could win a court argument suggesting that driver B felt compelled to act under driver A's suggestion. It was, therefore, driver B's decision to act and will ultimately be responsible for damages to driver C.

Cases where this may not be the case would be if driver A was a police officer or had some legal authority to compel driver B to act. But even in that case, it's highly unlikely that driver A would be determined to have any liability.