I rarely clean my brushes, so I can't imagine a trip long enough where I'd need or want to do it. But - they make wipes for cleaning brushes. Or I'd use shampoo (my own or the hotels) since that's usually what I do at home anyway.

There are also little silicone scrubbers. But I'd never pack one, probably wouldn't buy for home use either. Apparently I'm just not the demographic for this market ;-)