Haven't kited lake Eyre but have kited lake Lefroy WA
These two shots are taken from about the same place..
www.google.com.au/maps/@-31.3305915,121.7458518,190959m/data=!3m1!1e3?hl=en
There's a yacht club there apparently. Bit of info here on launching sites, wind directions etc: www.lakeeyreyc.com