Is there any way to run videos on Apple watch using Watchkit within my app? I tried finding any video player, but there was nothing. Thanks!
No - there's currently no way to run video on Apple Watch using Watchkit.
Depending on your desired outcome, you may be interested in the Animation capabilities of WatchKit. By adding a series of images into your Watch App bundle, WatchKit allows you to cycle through them at up to 120 fps or slower when fetching images from iPhone.
You could accomplish some pretty amazing results by animating images, although bare in mind image resources need to be kept to a minimum.
I suggest this tutorial on WatchKit Animation and this Swift framework for rendering UIViews as image sequences in WatchKit.