From what you posted above your firmware version is 4.0, but here's Amazon's help on determining software version...
https://www.amazon.com/gp/help/custo...deId=201177290
The 1308590058 is a build number I believe.
The firmware updates you want are here...
https://www.amazon.com/gp/help/custo...deId=200774090
That Kindle runs 4.x software so any type of 5.x software isn't going to work. The latest version for your device is 4.1.3
I don't recall if that device was supposed to have AZW3 support at launch (it came out around the same time as the AZW3/KF8 format did), but updating to the latest firmware should take care of things.