It's not odd...its actually quite expected...
Here's what I know. The traditional flasher for a bike is a thermomechanical electromagnetic switch.
There is a coil inside and a bimetallic strip. The current passes through the strip and it heats up (there is a set of contacts on that strip). Current flows into the strip and when it heats up, it moves from a closed (electricity passes to the bulbs) to an open (no electricity passes). If it isn't getting enough current flow (which you won't get with just LED's), it doesn't heat up (the strip) enough to open the circuit (flashing the lights off).
Here's how the circuit should be set up. Positive into the flasher. The ground from the flasher should be routed to the center terminal of the turn signal switch. One set of contacts should be routed through the left signals, one set through the right. When you set the switch to either direction, you allow current to flow (and current flows from negative to positive in a DC circuit) from the battery, through the light, through the switch, through the flasher.
With the switch you are just selecting which pair of bulbs the current path is through.
To use the LEDs...with a "no-load flasher" you have to wire like this:
Positve to flasher. Flasher neg terminal to "indicator" bulb (the 1156) Positive. 1156 Neg to turn signal switch center or common terminal. Turn signal Left to left LED positives, Turn Signal Right to Right LED positives...And of course...each LED to ground.
I can draw a simplified circuit for you...if you need. (by the way...Voltage is the "electron pressure" and is measured from Pos to Neg...but in reality, the electrons "flow" in reverse from Neg to Pos) Basic electrical principles.
When you choose left or right on the signal switch, you are completing the circuit through the required path (left or right).
Did this help?
Cheers!