Will the donkey tolerate having stuff rubbed on it? If it will you can mix Vaseline and powdered sulfur together to make a slimy yellow goop that anywhere you rub it on the animal insects will not go and because of its texture it sticks in place for days and water doesn't wash it off as neither Vaseline nor sulfur are water soluble. You can even rub it around their ears etc. just not their eyes. If you do this to a horse just make sure you don't rub it anywhere your saddle goes or your cinches go and so on. Works really well for rubbing on equines chests that get bit up badly by flies there. I do this for my horses anywhere riding tack doesn't go on them and I fly spray the parts that do. Works incredibly well for all manner of insects. It will also kill a ton of different types of fungal problems.
Absorb what is useful, reject what is useless, add what is essentially your own. - Bruce Lee