As per previous posts, flathead are common throughout the Australian coastline. I live in Melbourne, and these are one of my favorite fish to target 'flats style', by fishing early morning with a low around 0800. That way I can fish the last of the run out and the firt of the run in, as Harro suggests. I use clear wet tip fly lines when fishing from the shore, 7-9' leaders and either Clouser Deep Minnows or Bendbacks in very shallow water. You don't need much backing. When there's a strong current on a run out tide (such as Andersons Inlet in Victoria - take a look on Google maps) we use type IV sinking lines and fish Clousers like you would upstream nymphing.
Best outfits IMO are #7 to #9 weights depending on your fly size, wind and what type of flattie you're fishing for. In deeper water from a boat I'd be using fast sinking heads and a #9 weight. In Melbourne, I'll normally use a #7 or #8 weight nine foot rod. You don't need to cast very far because the fish are often in the shallowest water close to shore, particularly early in the morning. Start by working your fly in depressions, pockets, channels and the edges of weed beds, rocks etc.
Jumpy retrieves interspersed with pauses to let the fly drop work well. Carry a variety of colours and sizes from #2 to #3/0 (bigger flies for bigger fish mostly). Making your fly bump the bottom every so often seems to work well, but I know others say an unweighted Lefty's Deceiver works just as well. As you may have guessed, flatties aren't too fussy and are great to catch.
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