How can I update a user flag in rules?
My question: how can I fetch the previously applied flag in rules so
  that I can update the timestamp and re-save it?


Some good news but mostly bad.

If you add an extra text field to the flag and add an extra rule to set its data value to [flagged_uid]-[flagger_uid] when a flag is created, it seems that you can then fetch the flagging using that field as the Property and [account_uid]-[current-user_uid]. 

I say seems because while the rule runs without errors and I know my logic is right, I can't do anything to the fetched flagging to prove I've actually fetched it. I get an error when trying to delete it because "Rules doesn't have info about deleting a flagging" and saving it doesn't change the timestamp.

It just feels like it's not fully integrated. Even if you added a date field, I'm not sure Rules could access it on user view.



I guess I would either create a custom rules action to finish the rule or go with a fully fledged Field Collections solution.