Not needed imho
This is just my opinion, but I didn't use any thread locker on either end of the flap pushrods. The end that threads into the flap goes into a nutplate, so that's a locking mechanism on its own -- I did use an internal tooth lock washer there nonetheless. So that end ain't goin' anywhere. And on the top end, at least on the RV-7, there's an AN4-xA bolt going through an AN365 nylok nut -- that end's not going anywhere either.
As for the male rod ends that thread into the pushrod itself, as long as you have enough threads engaged on both ends, even if the locking nuts got loose, the rod couldn't come loose...it would rotate in one direction or the other, but bottom out before it came off the other end. And if you tighten the locking nuts, it's not goin' anywhere. And obviously you do inspect this prior to every flight.
You could use loctite on the threads there, but I would definitely use the "less permanent" type. That's just my opinion. Early on I did make an adjustment or two on the flaps.
Again, just my OPINION.