I ended up emailing the company and this is the reponse I got:
Dear Donna,
Thank you for contacting us.
We do not currently recommend any one product specifically, mainly due to our inability to test and certify the breadth of products on the market. However, we do have anecdotal information from consumers who have had success using various flash drives with their camcorders. Again, we do not endorse or recommend any specific product, but you might find information on message boards that attest to user success.
We apologize for being unable to provide you with a more definite answer, and we hope you won’t hesitate to contact us further.
Thank you,
Flip Video Support
Also this is listed on thier website Q&A section:
Can you recommend a product that I can use to store videos from my camcorder without using a computer?
Videos recorded by the Flip Video camcorder can be saved or moved to any type of memory storage medium. However, Pure Digital does not specifically recommend one memory product over the other, mainly due to our inability to test and certify the breadth of third party memory products on the market. However, we do receive anecdotal information from consumers who have had success using a variety of storage products with their camcorder. Again, we do not endorse or recommend any products, nor have we tested them ourselves, but you might find information on message boards or reviews that attest to user success with specific products.
So it looks like there is something out there that would work besides a laptop! I just would like to figure out what would work!