Just for the heck of it, I did a search for Fantasmic on KaZaA. Found 11 audio files (not recommended, since it's commercially available on CD) and 1 video file. So video, albeit unofficial, is out there. Good luck.
I have an old DL souvenir (from '95 or whenever Fantasmic first started) video with a fair chunk of Fantasmic on it. Since it is commercial, the picture and sound are excellent. It goes from beginning to end, but some of the in-betweens were edited out to keep the length down. Perhaps you can still find this video somewhere or on Ebay. I don't know if DL still sells a souvenir video with this clip in it.
The only good home video of Fantasmic I have is the WDW Disney Studios version. Email me if you want a file of that. My old home videos of the DL version are awful since I never got close enough to avoid heads and bodies (of the spectators in front of me, that is)
There have been 2 DL videos w/ the same approximately five minute long Fantasmic! clip to which Alex refers, both titled, "A Day at Disneyland - The Happiest Place on Earth".
The cover on the first featured this title however: "A Disneyland Day - Relive the Memories". It had a white background w/ pictures of fireworks over Sleeping Beauty's Castle, Splash Mountain, Pirates of the Caribbean, Main Street Station, the Main Street Electrical Parade, Sleeping Beauty's Castle in the daytime, and an overlay of Mickey and Minnie on it. The back had a brief description of each land accompanied by photos from each on the left side.
It was originally released in 1991, prior to Fantasmic!'s opening. The video was updated the following year for Fantasmic!'s debut. However, the front, sides, and end of the slipcase cover are identical on both versions. The only difference is on the back: the first had a summary intro at the top, while the newer version had a ups barcode at the bottom instead. I also seem to remember that the newer version's cover also glowed in the dark to tie in with other merchandise featured on the nightime Fantasmic! souvenir carts. Does anyone else remember this or is it just my imagination?
The video was updated again in 1993 for the opening of Mickey's Toontown, this time packaged in a plastic case that featured the title, "Disneyland: A Day at the Happiest Place on Earth". It sported a picture of Sleeping Beauty's Castle matted over a twilight sky in the background. The back had a teal background w/ photos of Splash Mountain, Big Thunder Mountain Railroad, Mickey in Fantasmic!, and Mickey in Toontown.