Following these steps should get it to work for you:
1. Copy the AVI to templates (as you have already done)
2. Also copy the AVI to the same folder as the dialog (.DFM file)
3. If it does not already exist, create a plain text file with the file name of the dialog and the file extension .DFM.BAGGAGE file (ex: mydialog.dfm.baggage) with the name of the AVI file (ex: myavi.avi) on the first line of this text file and nothing else, save (ex: in Notepad)
4. In the dialog editor, in the FileName field, enter the name of the AVI only - NO path information (ex: myavi.avi), press ENTER
That should do it! If you're confused about baggage files, take a look at the built-in themes Attractive, Titanium, Emerald, Swoosh, etc.