I was there last week on a family holiday. We visited Mainland, Rousay and Hoy.
Looking around with wild camping in mind I didn't think it was 'promising' territory. The low ground is all enclosed fields with stock. Maybe a few places on 'scrub/spare' bits of ground at the sea shore ?? I'm sure farmers would be OK if you asked to camp in fields - but is that what you want ??
There is open/hill ground but I'd not want to try pitching a tent anywhere other than high up where the vegetation is arctic/alpine. The heather grows deep and thick at lower levels - due to the lack of deer grazing. I had a great walk on the tops on Hoy but almost no suitable places to put a tent - even near rivers there is just no open flat green spaces. April to July is bird nesting time so open moorland is probably a no-go anyway - You'd get seriously 'Bonxied' .
Some places that might be suitable around deserted crofts and abandoned townships. Too much agriculture to rely on using water untreated from the burns.
The other islands we didn't visit so ??? - Sanday looks a better prospect.