^^^ Climate matters.
In my view, a chicken coop isn't a people house. You won't be walking on it, if the roof collapses under massive load, the costs aren't irrecoverable (human lives lost, all contents destroyed). Therefore, there is no need to build the roof of a chicken house to Miami-Dade Hurricane Building Standards, or the 2018 International Residential Code.
Even for moderate loads on moderate spans (there are places where persistent heavy wet snow loads need to be specifically engineered for), which covers most all of central and southern US, plus chunks of the north, 2x4 rafters set 2' on center on top of the top plate with a few hurricane ties is adequate for load support, with 1x4 or 5/4 x 6 purlins set every 18 x 24" oc. No plywood needed, 5v style (or similar) sheet metal roofing screwed directly to the purlins. Its cheap, its fast, and if you ever get a water leak, its easy to locate for repairs. SHould you be in particularly cold climate and need some form of moisture barrier against frozen condensate forming on the underside, then dripping on your birds, tyvek or similr housewrap can be stapled to the underside of the rafters. Miosture vapor will pass thru, moisture droplets generally will not. Sadly, tyvek and other house wraps can become clogged with dust, in time.
Roof pitch is typically 3/12 (the minimum recommend from any mfg to adequately shed water without special underlayments, regardless of roof type) to 5/12. Pitches in excess of 5/12 may be useful aesthetically, but are not resource efficient - you spend as much (or more) of the length of each panel gaining height as horizontal coverage, and that height has almost no value to you for chicken keeping - particularly as it comes at the expense of steeply sloped sides of limited usefulness, and a taller profile for lateral wind load concerns (something to keep in mind particularly with top heavy raised coop designs not anchored into the earth).
and even with such underengineered (by people house standard) rafters and purlins, you can still safely walk on the roof for occasional maintenance if your body weight is in the 200# +/- range with comfort. If you are pushing 300#+, I'd be a bit more cautious.