To my understanding, Kindle Fire is based on the linux kernel so there would be no antivirus product necessary. It also, as I understand, uses a sandbox keeping the Operating system distant from any running applications. The more worrisome security issue would be, I think, the necessity to have an active amazon account with CREDIT CARD information setup for purchases with just one click.
You might be fine using it, but if you lose it or if is stolen then you might be minus more than the kindle fire...it just might be kindling for a much larger fire.