I'm not an electronics expert, so I can only point you in the right direction. I don't know anything beyond this...
LEDs draw much less current than an incandescent bulb. I'm pretty sure our flashers are thermal, which involves a metal contact that heats up and cools off repeatedly, causing it to cycle on and off. With an LED "bulb" in the circuit, there is less resistance in the circuit, so the contact heats up quicker and the flasher flashes faster (say that three times fast). Same thing happens if the regular bulb burns out.
The "bulb out" test also wants to "see" a specific resistance in the circuit. Again, the LED has less resistance and will cause the warning to come on.
The solution is to wire a resistor of the correct Ohms and wattage in parallel with the bulb. I have no clue what the correct value is, but there are simple formulas for determining resistance in a circuit. You'd just need to measure the resistance of the original bulb and subtract the resistance of the LED "bulb" and use the formula to determine what resistor you need.
There are also companies that sell inline resistors for this purpose. Here's one I just found with a search. I have no idea of their quality:
http://www.v-leds.com/BlinkerWarning-Fix/c132273/
Much better than cutting the wires permanently IMO.