Flags are used mostly for troublesome or problematic comments. You give them by clicking the “Flag as…” link beside a comment or question, then fill out the submission form. Those are sent to mods who can choose to delete or leave the comment as is. They do not affect the score, they only serve as a way to delete spam or off topic comments.
I am glad that there is no way to find out who favorites your comments or questions or who flags your posts. Such information would not contribute to the primary purpose of this website, to answer questions, and may in fact encourage petty squabbles.