The wheels should be available. I believe they are a standard size for American Flyer, both Gilbert and pre-Gilbert Flyer. The steel axles that hold the wheels on should be pressed/hammered at one end to create a lip that holds the wheels on.
The method I use to replace wheels is to use a hammer and destroy the existing wheel on the side that is pressed on. Then use a hammer to pound the small lip flat all the way around the axle, so that the axle is free to slide out of the bracket that holds it on. Slide any remaining old wheels off. Make sure you don't file the lip off of the axle.
I believe that the replacement wheels have a slightly smaller opening for the axle to insert into. Therefore, the hole has to be drilled out slightly larger to fit the axle through. Once the wheel opening is re-sized, slide the new wheels on and then use a hammer to pound the end of the axle to create a new lip to hold the wheels on. Make sure you do not use too much force on the hammer, or you will bend the axle.
NWL