Since installing new flush valve, the toilet increasingly (randomly) is surging as it fills. Is it likely that the flush valve is allowing air to enter the system; it appears to be functioning properly?
Our well service company said our pressure tank is not the problem, and the other two homes on the same well are not experiencing the problem.
I have tried bleeding all the pipes in the house to remove any air that may have gotten in the system, but the problem persists. I am wondering if the process I used to bleed the lines was correct; for instance, do I shut off the water supply to the house before opening the faucets to bleed the system, or let all the faucets open and running?
The surging is loud enough and strong enough that we are concerned that damage to the system's pipe and connections may result. Any help/advise will be appreciated. Thanks.

Go to each plumbing fixture, Open Hot and Cold water and let it run for few minutes. Leave water supply to the house Open. That will bleed the system.

You can also close water, remove toilet supply connector at the tank and run water through this connector into a bucket until you get air-free flow. Then, reattach water supply.

Plumbing system in your house is closed system and it is pressurized. It doesn't "suck" in air on its own nor does the new fill valve randomly allows air into the system. It looks like you have trapped air in pipe somewhere by the toilet.

Back to you. Milo

Any air in supply lines should automatically be expelled as soon as you open a faucet.

Sounds like air is being introduces by well system. A well system that services multiple residences would have necessity be complex with a number of controls.

One way is to have a large pressure tank with piping to each residence. This is the simplest but requires a very large tank because the pressure tank is not very efficient in storing a large volume of water. Another way is to have a large storage tank with float controls for the well pump. This would require an additional (smaller) pump and a pressure tank at each residence. Any other way would require very complex pump controls.

Please describe the well system.
You indicate that you have at least a pressure tank, do you have your own pump? What kind of tank, bladder or galvanized pressure tank? If you have the galvanized pressure tank, is it equipped with an AAC ( automatic air control) valve?