Flagrant and blatant are very similar in meaning as in doing something bad conspicuously./ in a obviously bad way
Flagrant is stronger than blatant in that it attaches a sense of doing it willfully especially when knowing that is bad or it is it so obvious that it cannot escape attention/very noticeable
His father is powerful , so he can behave flagrantly.
The mistake he made is so flagrant that a simple guy can see it.
He blatantly display his wealth ( show his wealth unashamedly)