Hey blackdeathtrap,
If that is the actual flasher you ordered, I don't think it will work. From my experience with
my car, I needed a 2 pin relay.
I am pretty much in the same boat as you are. I have changed every bulb that is on my car inside and out to LEDs including my headlights. I have the same issue with my turn signals as you have (they are staying lite up (solid) as though the bulbs are blown). This is due to the little amount of current draw / load that the LEDs exhibit on the system. The LED bulbs use about 1/10 of current draw as the stock bulbs do.
You will need a 2 pin flasher (electronic). I got on from o'Reillys and it worked perfectly with the tail light LEDs. But when I put the LEDs in the front lights (2057/1157 locations), the solid turn signal problem came back.
I found out that you will need the LED Electronic Flasher p/n CF12ANL-01 that was not available locally here, so i ordered one online. It was supposed to be here last Sunday, but got lost in the mail. I should have my new one here on this Friday.
Note: the electronic flashers work silently, So there is no clicking sound when the turn signal is activated. The stock ones are mechanical which give you the clicking noise.