I have done a lot of light upgrades on heavy trucks and auto applications over the years. Are you running LED lights front and rear on the turn signal circuit? If so, install an inline resistor in your circuit for the turns. This will mimic the resistance that the older style bulbs (filament) create, and your flasher should work just fine.
You can also attempt to use a filament bulb on the front, with an LED on the back with out the inline resistor. However, that may sometimes lead to a hyperflash condition because the body control module thinks that the rears are not working because it doesn't sense enough resistance.
If i remember right you are using an early/mid nineties GM chassis. How much of the wiring are you using from the donor chassis?
well, any way. I always got my inline resistors from radio shack.
Sometimes i only needed two, (for vehicles with out a body control module), I would mount them in the circuit to the front, (4 LED system), and it would work just fine.
If you have a body control module, you will need four. I mounted a resistor, in each turn circuit to eliminate the hyper flash syndrome,or no turn at all.
You need the resistance to get the flasher unit to work correctly. With out it, no flash.
If this is as clear as mud, feel free to PM and i will try to trim down this landslide of info to your specific application.