You can use the API for this. The documentation is good.
In your case you'd use
/me/associated), this will return badge counts and reputation for all sites you are on. You can reconstruct the flair info this way.
items array in the returned object will have an item for each site that looks like:
"site_name": "Stack Overflow"
For your usage you'll probably want to set the
pagesize to its max of 100 and don't forget to honor the
has_more parameter to support > 100 accounts. See paging.
For the profile image it's site specific, so you'll have to use
/me) with the desired
site parameter to get the URL of the avatar.
For details on specific sites you can use a lot of different things, just look under the Users section of http://api.stackexchange.com/docs. Each function is described there and the returned objects are described in every doc page, you'll be able to find whatever you need.