In most countries, revolution must be prescribed by a vet. In Australia I think you can get it without a prescription but I’m not sure. If you can, you can treat him with it at home safely, I think there’s a variety for kittens that is recommended for rabbits.
What I did was treat my first bun with permethrin, but this is not always tolerated by all rabbits. I used a minute dose of Ex-spot for dogs, just the tiniest droplet, at the nape of the neck where the problem was at its worst. I did this because a breeder of show-rabbits told me she uses this with her rabbits when they get mites.
It worked fine. I repeated the treatment a few weeks later. The mites have never come back. My second bunny also had mites (Cheyltiella parasitovorax) when I found him. I treated him with Ultra Shield for horses and dogs, it also has permethrin but in a much, much lower concentration. I had to treat his affected area once a day for a few days before all the mites were gone. They’ve not come back. Neither of my bunnies had any adverse reactions to the permethrin, but as I said earlier, some rabbits do and then you have to shampoo and bathe them right away. Dogs and horses can also have adverse reactions to the stuff even though it’s meant for use on dogs and horses. This would be the budget-solution if you haven’t the money or ability to take him to a vet for Revolution.
What you absolutely must NEVER do is use Frontline (fipronil). It is lethal to rabbits and the manufacturer warns against using it on rabbits. It would kill the mites but probably the bunny too, so DON’T use that!
Mites of this variety are very common in rabbits that’s been under stress of some kind. Bathing the bunny with regular shampoo won’t help. Oil etc may help you comb out the flakes and perhaps soothe the skin, but won’t kill the mites.
I realize this is a bit controversial, but it is a remedy widely used by (show) rabbit-breeders in Sweden. If you have like 25 bunnies housed outside they will get mites now and then and it’s not affordable to go see a vet with them every time.