How can I log the flags users put, then auto unflag them?
The Log 

Userpoints transactions are automatically "logged" in that Views can display them with all required data. So if I understand the question correctly, flags is irrelevant here in terms of logging as you just want the userpoints transactions.

Create a "userpoints transactions" view.. Not "content" or "user".


Add a relationship for Userpoints Transactions: User  
Add fields for
(Users) User: Uid (Uid),
Userpoints Transactions: Timestamp (Timestamp),
Userpoints Transactions: Points (Points) and
Userpoints Transactions: Entity ID (Entity ID) (according to your link, this should be the node id)
If you have more than one category of userpoints, you can add a filter for Userpoints Transactions: Category


Automatic Unflag

It sounds like in your link, Business Rule 2: Unflag an item is unneeded in your case? I'd just change this to a rule where the the flag is unflagged and then redirect to the node / page if needed. I'm not really sure what the requirements are here.