I wear a longish beard these days (currently 6"), and have periodically been irritated by itchy skin and even "beardruff." I've got it figured out now:
(1) Shampoo the beard with "Nizoral." It costs a bit more than regular shapoos but if you use just the moderate amount that you need, it lasts a long time.
(You have to rub it into the skin and give it a couple minutes there before washing it out.)
(2) Shampoo the beard with this as frequently as necessary. If once a week doesn't cut it, go to twice a week. If twice a week doesn't cut it, go to every-other day. In an extreme case (probably unnecessary) do it every day. It will work, you just need to systematically increase frequency until you dial in the right interval for your face.
(3) Never fail to apply beard oil after every shower (or any other time your beard gets wet), while the beard is still damp (not dripping, but still a bit damp). The oil is both for the hairs and for the skin -- make sure to rub it into the skin a bit, especially where you get itchy.
(If you want a pre-made oil, Honest Amish is about the best bang-for-buck. I make my own and I'm happy to share my recipe if anybody cares.)
Hope this helps!
Scott