It stores your recordings and the log files on a HDHomeRun folder in the recorded TV public Library that should be at the top of the explorer under favorites. I have done two test recordings so far of PBS's Auto Week through Kodi in windows and Android.
The recordings play great and look fine, are in MPG HD format and should be editable with anything that can handle it like video redo. I don't think it supports protected premium channels yet but anything copy freely and not protected should work.
Like said it's a very early beta just to prove it works and get people using it to ferret out bugs and slowly add features.
Sooner or later a Windows, Android and Plex version plus others that will support DRM should be out but might take a while, gotta walk before you can run.
Folks are also asking for a grid style EPG and that will probably eventually happen too to make life easier.
So far all I have to do is pick a show or movie I want to record through Kodi and once everything's set up it's hard wired into the Prime and Kodi does not have to be running, though the PC needs to be awake when the timer event happens supposedly, as it wont wake it up to record.
Don't know for sure as both times the Autoweek came up it recorded it but the box may have already been busy doing something and awake. It doesn't give a lot of options to record yet, just everything and recent but it seems to default to HD only if several SD and HD versions are on at the same time.