The best practice for squirrels is the same as for other rodents, sanitation, exclusion, or elimination, in order of cost and effectiveness.
Squirrels are tougher to stop than rats but IF you have mostly full size hens and mostly adult birds you can set the door springs stiff enough to stop one or two squirrels if they gang up. And if they do break through by overwhelming the feeder with a bunch of tree rats the inward swinging door makes one heck of a squirrel trap. The will be trapped between the door and the inner angled feed tray. Lift the treadle feeder off the hanging cleat, dump the feed into a plastic bag or clean barrel, then either take the tree rat for a long ride if your state allows transporting them or dunk the feeder in a trash can of water for ten minutes before fishing the critter out or unscrewing the door.
But the three methods... Sanitation, treadle feeder, a good one with a narrow and distant treadle, spring loaded door that swings in, the other kind are useless once the squirrels figure out where the feed is. Clean up all the pathways the critter is using to come and go so it faces natural predators while traveling. Bulk feed in metal drums with tight lids. Going to cost you a couple hundred bucks for a decent feeder and a metal drum and a little work.
Exclusion, the Ft. Knox chicken coop. Hardware cloth 360 degrees, no free range, no holes over say a quarter in size. Expensive....
Elimination, never ending, be it poison or trapping or killing. Once removed a new population will take over the vacant territory anyway. But it can provide brief periods of relief.
By rock squirrels, I am assuming they are more like chipmunks, not regular full size squirrels? Chipmunks are lighter and weaker, easier to exclude with a treadle feeder.