The blinker system requires the correct load to operate properly as the current drawn by two indicator bulbs causes the bimetal strip to heat and bend (making and breaking the contact). If the load is wrong it will not heat enough and therefore will not flash.
As the RH side works, there is nothing wrong with the flasher unit (as there's only one of them in there!)
You must have a blown bulb (or bulbs) or a fault in the wiring.
Swap bulbs R to L first.
Check the green (earth) wires that come out of the lamp assembly. Are they connected to the frame?
Report back.