Using source, I have found out that
1] Instagram saves pictures in :
igcdn-photos-<x>-a.akamaihd.net/...
2] Facebook saves photos in :
fbcdn-photos-<y>-a.akamaihd.net/...
How can I use this information to get the facebook profile of an Instagram user, assuming in today's world, 90% chances of FB and Instagram profiles being linked...?
You can´t, and you shouldn´t. Those are different platforms (even though Instagram is owned by Facebook now). If you want to link a platform to a specific user, authorize the user on Facebook (or Instagram). You are only allowed to use the profile picture if the user allows it, so the authorization is not really a problem.