In Dropbox on iOS you have the option to "make file available offline" and "save video". To access the file you will need to "save video".
You can do this with the following steps.
1. Go to the file you want to save in Dropbox.
2. Tap on the icon in the upper right corner (the box with the arrow - not the 3 dots).
3. Tap "Save Video".
Once you do this the video will be saved to the photos on your device and you will be able to attach it to a tag.