I spent several years clipping parrot wings. Takes two people- one to hold that strong beak! Anyway- our goal was not only to limit flying but to allow safe landings if they did try to fly. One wing tended to throw their balance off, increases risks.
One person safely held the bird. It had to be safe for the bird and the two humans. Not as much of a problem with chickens but it still must be safe for them.
The person trimming first checked the wing for any blood feathers. Those are the ones that will bleed. If you do cut a blood feather and it starts bleeding-remove that feather (hemostats help) then apply cornstarch. By first checking for blood feathers even before looking the bird over for trim lines we had no accidents.
In most cases we left the first two flight feathers alone for asthetics. For active light birds we didn't as they were more likely to fly. Since we trimmed both wings we did trim further back the wing than most others. Once we trimmed one wing we repeated with the other then rechecked both wings for bleeding, equal trimming, etc. Then on to beaks and nails.
With practice, a lot of birds will learn to fly and/or compensate whether it's one or both wings. But with both they usually had a safer landing- no thuds of bodies hitting the ground or flying into objects. Chickens usually fly down from their roost at least once daily, it would be nice if they could do that safely.
Would putting a slanted fence lip on the inside edge of a fence reduce fly outs? Like they do with cats (and prisons). You'd only need to do 2-3 feet of fencing in from the fence.