As previously introduced, flat Majors are Major chords which are outside (in between) chords in a Major key center. They sit in the gaps between diatonic chords of a key. We get their names by comparing to what is ‘normal’ in Major keys.
In C, the normal E type chord in C Major is E minor. If we flat it (lower it one half step), and make it Major (basic Major triad), it can be viewed as a ♭III [uppercase III is a Major chord in letter position III]. This is a Major chord built on the lowered 3rd of the key. Same for the 7. The normal 7 is B diminished. Flat it, make it Major…B flat Major.
The complete flat Major sequence is ♭II, ♭III, ♭V, ♭VI, ♭VII. In C, these chords are D♭, E♭, G♭, A♭, & B♭. There is no ♭IV because this chord would be F♭, which is E Major, and E is in a different class [it’s a secondary Dominant = V/vi in C].
Flat Majors are most common in rock music. A great example of flat Majors in action is the band Linkin Park.