Adam, Flathead are the best fish to start with on a fly. You really don't need a sinking flyline as such. A floating line is fine and much easier to handle. fish the edges and pockets in weedbeds as flathead love to ambush small fish etc.Most of the really big flathead I have caught on fly came from less than 1 metre of water. Your fly just needs to be near the bottom. Patterns such as Clouser Minnows or Crazy Charlies are ideal. What weight rod are you using? I would use a heavier tippet up around 12 - 16 ib. Flathead are not leader shy as such but they do have lots of small teeth that will destroy fine tippets.
Wade parallel to the shore, cast along the edges of weed beds and just strip the fly back with a short steady retrieve. you don't need to cast a mile. Whats more important is to work the water in front of you. Long casts may look wonderful and its great if you can make them but a 30 ft cast will catch just as many fish. Drop me a line if you have any questions