Interested to read about this. I have my duck aviary roof sloped, but no guttering. Probably would be useful so rainwater doesn't drain into the aviary from the back.
I use clear corrugated plastic roofing sheets but I'm trying to think of other options because the sun makes it get brittle pretty quickly (maybe not an issue in the UK). I'd also prefer not to have to use plastic and I'd like whatever I use to last 10+ years and through high winds (this stuff is pretty good with wind though).