According to this archive readme, Flash Player 9 from versions 9,0,16,0 through 9,0,47,0 function on Windows NT 4.0:
Flash Player 9 Archive Readme.txt
You can get these files from the links below, or from Adobe Archived Players page: Archived Flash Player Versions
I am personally using Adobe Flash Player 9,0,47,0 for Firefox and Opera under NT 4.0, and Flash Player 9,0,47,0 for Internet Explorer 5 / 6.
I have tested this myself on my NT 4.0 system and confirm YouTube and other websites function with no errors.
The by-now dated flash player 8 I provided above a couple of years ago may crash or may not run.