You can, and you can do it in a way that avoids the flicker (by the way, the flicker happens when the fogs are turned off which seemed weird to me.)
Anyway, here is what I did. I cut the factory harnesses off by the bumper. I tied the factory power leads to a new single wire and ran that wire to the switch spot on a new SPST relay I put up in the engine bay. I tied the factory ground leads to a new single wire and ran that wire to an appropriate ground bolt (use the frame or one of the existing ground bolts in the engine bay. From there it's pretty easy. Relay gets grounded and also gets fused power directly from the battery. Remaining spot on the relay is the wire to actually turn the new lights on (hot lead on the new lights.) Obviously the new lights also get grounded to the frame.
If you have ever wired lights before using a relay then you should have no issues. All you are doing is using the existing factory fog light power lead as the trigger for the relay.
