I think this really depends on how the Flash file is designed/coded... so there isn't really any specific advice we can give you without looking at the source .fla.

Have you considered trying to hide the button, rather than removing it completely?

Update:

I asked the author about removing the button. He said this:

"Make a modification on one of the movie clips in the fla library. It's called RightButtonPanel. Open it by double clicking and remove the full screen button. After doing this, go to the src directory, open PhotoGallery.as and remove the full screen button reference in the init function. Save and recompile."

Fine. I did that...8 times with variations. But again, once I remove or delete the button the site will not load.

Then he asked this.
"Did you add the src directory to your classpaths? Does it successfully compile?"

Yes I did, but how do I compile it? I thought by hitting the "publish" button it should work. When I publish I am warned about a missing font and asked if I want to override something-or-other. It doesn't matter whether I say yes or no. It still won't work.

Can anyone please tell me about compiling src's and classpaths in Flash?