That is an LED compatible flasher unit. I've had both types installed on my truck running a complete LED system. Let me ask some more detailed questions.
I know you put the LED bulb in the blinker switch but have you tried them with the bulb removed completely? Some newer LED bulbs are designed so that polarity doesn't matter. If you happened to unknowingly use one of those it would be the same as having an incandescent bulb in there. We are wanting power to only flow in one direction, hence the use of an true LED.
Have you verified your wiring connections were correct? I originally had a set of Truck-lite LEDs in the front and the tags on the light wires matched up perfectly to the truck wires. A couple of weeks ago I swapped to Grotes in the front and the tags were correct on one but not the other. These lights are used on many vehicles so the tags could be wrong. First figure out which wire goes to the BO light then swap the other two power wires and see if that makes a difference.
What brand lights did you get? Newer Grote LEDs have built in load resistors that should make them compatible with all flasher units, theoretically. Truck-lites don't have these. There are other manufacturers, Riverside for instance, that I haven't dabbled with. It shouldn't matter with the flasher unit you have but I'm curious of the manufacturer all the same.
Is the flasher unit on the firewall grounded well? The wire going to the bolt on the left in your picture is the ground for the flashers. That looks a little rusty. That ground might work fine for incandescent but not LEDs. That ground terminal is using the bolt for ground, which threads into the firewall next to the PCB, not the flasher itself. The threads need to be clean on the firewall.
You did use the extra wire on each light to properly ground it, correct?
Do all your other light functions work correctly on the LEDs; brake, parking and BO?