I haven't played that campaign before, but what I usually try to do with helicopters is to try sending one or two scout helicopters along the planned flight path of my transport helos to try and get any AA capable units to reveal themselves. I move in short spurts of 5 hexes or so, so that even if I don't spot the firing unit, I still have a pretty solid idea of where the fire came from.
Then, I reroute my transports to stay 3-4 hexes away from any enemy units (taking care to scout out my alternate route(s) as well. This usually works to keep losses of helicopters and airmobile forces to a minimum. If I have no scout helicopters available, I try to pick one of the fewest units on board (preferably one without a platoon leader or heavy weapon) to act as a fire magnet, erm I mean scout

That way, I keep my losses to a minimum.
Careful selection of an LZ is also crucial. Often I have found that a great looking LZ near your objective hexes will be well-guarded by enemy units. For this reason, I often try to prep the "perfect" looking LZs with artillery and smoke on the turn before landing. If the LZ is still too hot, I either select an alternate LZ nearby or hold off a turn while I call in additional artillery fire (which, since I just used it to prep the landing zone, is already zeroed in and can quickly deliver another barrage).