Our donkeys had a bad reaction to a pour on product a few years ago, never to be repeated, it took off a load of hair and left angry, sore skin.
Sudocreme as previously mentioned and a skin scraping if you suspect any mites. Also a vet the understands donkeys is a boon, ours is very good and understnds the differences from horses.
Ours love a roll in the dirt usually as soon as we brush them! Also as previously mentioned they get a bit manky when the shed their winter coat for summer. If you are regularly running your fingers through there coat when having "donkey time" you will see their coat has a "dust" in it and this comes off on your fingers like a lanolin type substance, it's just the natural oils in their coat.
Also they do occasionally have a wee nip of each other and can pull a bit of hair out when they do that!
Hope that helps.