Here is how you can quickly download videos from Twitter for your personal use.
Just open the Tweet with the video. Left click any part of the preview video before it starts playing to copy the link. If you are using mobile device. Just press down any part of the preview video for a 2 or three seconds to copy the link.

After copying the video link, proceed www.downloadtwitter.video and enter the link in the download bar then press download to download the video into your phone.