If one side flashes, the flasher is good. You can swap the 4-way flasher in to try if you really want to, but that's not it.
Three possibilities come to mind. Bad wiring to left signal, bad switch or my favorite, bad ground. If it's both front and rear, chances are it's the turn signal switch, but some time with a shop manual and a test light are in order before you go to the trouble of changing the switch. If it's just the front (or rear) I'd look at grounds.
If you are checking for power AFTER the flasher, there has to be a load on the circuit (like the light).