Thanks, I didn't know about dope! Synthesising nitrocellulose or cellulose acetate seems to involve quite a lot of steps, so that's out. Wikipedia says that before nitrocellulose etc. were used, people tried sago starch and rubberised fabric, and this wasn't very good. Since I can't find anything on how easy it is to make rubberized fabric, I guess I'll go with sago, and maybe mention that the aircraft need to be re-starched frequently.
Right, I wasn't thinking of ornithopters! Just that knowledge of aerodynamics sufficient to build functional aircraft could be obtained on a timescale less than several hundred years, by discussion with the birds and the wind.