I'm with gimruis here. Experience is the best teacher. No substitute for seeing lots of pheasants.
So when I started out chasing pheasants, before I had a dog even, I would pace the distance to the flush whether I shot or not. The bird just flushed, I had a picture of that in my mind and I'd step off the distance to figure out if it was in or out of my particular killing range. Same with the fall; if I dropped one I'd pace the distance to the bird for the same reason, to correlate picture with range. Do that enough, you gain experience in judging distance.
I watched a Randy Wakfield video on a 60 yard pheasant shot. Modern times; he carries a laser rangefinder to determine distance to the fall. I guess that would work for distance to flush too and save all that pacing.
On other thing that might help on judging distance. NRA makes a life size pheasant target. You could buy a pack and post them around the yard at various distances so you could get familiar with what they look like at various yardages. Midway has them for about $30 for a pack of 25. Might come in handy at the pattern board for load/choke testing at various ranges too.
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NRA Official Lifesize Game Targets Pheasant Paper Pack of 25 (midwayusa.com)
I DO shoot a lot of clay. I'll probably shoot somewhere between 1000-2000 rounds before next season. Skeet, Trap and Sporting Clays. Most people shooting Trap from the 16 yard line are breaking the bird around 17 yards or so from the trap. Call it 35 yards. Most Skeet breaks are 20-22 yards if you break the bird around the center post.
I don't shoot these games for the game or score; I shoot to get ready for hunting. I'm fortunate that I have a range nearby where I can shoot gun low without people getting their nose out of joint. So my breaks are a bit farther out than that. I think it just helps me with making my gun mount better and is more like a hunting situation. Anyway, yeah, I screw up a gun mount, I miss for other reasons. Sometimes I'm in the teens. But I keep practicing until I'm pretty consistently in the 20s. It's true that clay breaks easier than pheasants die. But I you can't pretty consistently bust a 35 yard trap target you aren't ready for a 35 yard pheasant going away shot either.
As always, Your Mileage May Vary and I certainly respect your right to disagree. This is just what works for me and may not work for anyone else.