You can flush a toilet with a well without electricity but only with the water that is in the toilet tank and the leftover water in the well pressure tank.
Well pressure tanks vary in size and some hold 1 gallon of water and others hold around 10 to 40 gallons of water.
As long as there's water in the well pressure tank, then the well pressure tank will provide water pressure to the toilet and plumbing inside the house.
So you could flush the toilet a few times until the well pressure tank is empty.
One the well pressure tank is empty then you won't be able to flush the toilet unless you have some water in buckets.
It's a good idea to keep some buckets of water for flushing your toilet in the event of a power outage or problems with your well pump or well tank.
The well pump needs electricity to run and you could use a generator when hooked up properly to run the well pump when you need water.
I had my well pump system wired into where I could plug my generator into it and flip a switch to switch over to generator power so that I have water in a power outage and I have some electricity as well for the house.