The above is probably a definition of a clear footfault, but flagrant seems far stronger than that.
: conspicuously offensive <flagrant errors>; especially : so obviously inconsistent with what is right or proper as to appear to be a flouting of law or morality <flagrant violations of human rights>
A flagrant footfault would be one that is both an obvious error from the viewpoint of the receiver and one that was intentionally committed so as to flout the rule.
Its my guess that the flagrant footfaults that the USTA eventually allows you to call are not just breaches of the rules, but ones where the clear intention is not just to cheat - which implies a concealment of fault -
but an attempt to cheat with open contempt of the rule.