I'm no expert...
I caught my first Iowa walleye on fly gear while drifting a black microjig from my kayak earlier this year.

Then I went on a fishing trip to Ontario, Canada and caught 5 more on fly gear. Fortunately, the fish were in water only 4'-10' deep, so I could use either floating line or sinking line.




I echo the fly choices mentioned by others above....Clouser Deep Minnows, Bunny Strip Leeches, etc.
Here's a picture of some of the exact flies I caught walleyes on (except the top and bottom patterns, which caught perch and pike, respectively):