Hi Microraptor_Gui. Welcome to the forums.
Is there a way to include a flash .swf file in a jQuery slideshow?
Yes, there certainly is. Most slideshow scripts don't care what you put in them. They basically just slide/fade in one element after another, such as divs, and you can put whatever you want inside those divs.
What video file format would you recommend?
It's fine to use Flash, but it won't work on some devices, such as mobile Apple devices. An alternative these days is to use the native HTML5 video element. There are various ways to use it, such as providing one file format (mp4) with a Flash fallback for browsers that don't support that, or having two formats (mp4, webm) with or without a Flash fallback.