Is it a Mac Classic specifically, or do you mean to watch videos on a "compact Mac" of any type?
The Color Classic can play old-school Cinepak and Sorenson codec QuickTime videos just fine.
The (black and white, 68030-based) SE/30 and Classic II can be cajoled into playing video with some effort.
The 68000-based Classic, SE, Plus, and before are completely incapable of playing anything approximating video.
You will *NOT* get any copy of Flash Player to run on any compact Mac. The first version of Flash to support video was in 2003, long after any 68K support was dropped.
If you were to dig up a positively ancient copy of Macromedia Authorware, you could create a video-like presentation.