To download a video from Twitter you can use one of the following sites.
Both sites allow you to enter the URL of the tweet that contain the video. However, if you want to download a video from a dm or message you will need to try something different. You can use Firefox and a extension called Video DownloadHelper.
1. Install Video DownloadHelper extension from your Firefox browser
2. Install the Companion App from the Video DownloadHelper extension general tab
3. Open the Twitter message containing the video then click on the Video DownloadHelper icon in the top right. You will be given several video resolution to choose from.