Um, not if there is a password?
Usually you can try passwords until it tells you you need to re-enter your Google Accounts password... but not on a Kindle Fire.
If USB debugging was enabled, then you can access the files using ADB (Android Debug Bridge) -- according to
HERE it is enabled by default (terribly secure, huh?
).
Otherwise, there is a problem... by design, these devices are programmed to secure your data from thieves -- that also locks out people who just want to return the device, as well as people who inherit them from a family member who passed away.
Any way of retrieving the data might then require forensics -- although if you can pull apart the device and read the filesystem from another hardware system, that is one way to circumvent virtually any protection.
Any help you can get from Amazon will only relate to securely wiping the device so another person can use it from scratch.