I know this isn't clearly communitcated in the app but Amazon Logistics isn't really meant to be used as a manually created entry. Instead, I recommend creating a normal Amazon.co.uk entry which requires less information (or use the synchronization feature to not enter anything). The default Amazon provider will then automatically detect the Amazon Logistics tracking ID and add it as a partial delivery with all required information filled in.
The "Provider" field is a specific code Amazon uses to identify the actual shipping type. For Amazon UK this can be one of the following:
AMZN_UK_AGEVER, AMZN_UK_ECON, AMZN_UK_LOCKER_PRIME, AMZN_UK_PRIME_HAZMAT, AMZN_UK_PRIME, AMZN_UK_SAME, AMZN_UK_STD
There's probably more than this but this is just to get you an idea. You should be able to find this code in your Amazon tracking information on the website but as I said you shouldn't need to bother with this.