Auto Play for videos is a feature that is being restricted by some browser and device makers, so you may run into issue with it.
Check to see if if your is video muted. Often browsers all either sound or autoplay, but not both.
Check to see that you’re using the “FlexSlider” option for your slideshow. The “Responsive Slides” option does support video. However, due to the limitations of Responsive Slides, Auto Play is automatically disabled when you add a video to a slideshow. Responsive Slides is a very small slideshow library, but it doesn’t offer a way to pause the slideshow once a video starts playing. Due to this, auto play is disabled automatically when a video is present in the slideshow. This ensures the slideshow doesn’t move to the next slide while a video is playing. The FlexSlider library does allow you to pause the slideshow while the video plays, then resume the slideshow when the video stops.