The first scale is just the standard F major scale:
F G A B♭ C D E F
The reason the standard F major scale is used over the lydian mode for horizontal playing is that the B♮, unless resolved upwards, can sound out of place against other chords in the key.
Russell's F major flat seventh 'scale' is the mixolydian mode relative to Bb.
In the key of B♭, the seventh degree is F. The seventh chord built off of F in Bb consists of F A C Eb, and so the most consonant scale choice will use E♭ instead of E♮.
B♭ C D Eb F G A B♭ C D E♭ F G A B♭
The F major augmented fifth scale is a bit peculiar for a couple of reasons.
F G A B♭ C♮ C♯ D E
Clearly, the C♯ is is going to fit better with chords with a raised 5th.
Something that is obvious but should be stated is that a scale or mode to be played over a chord or sequence of chords depends upon the specific chords and how dissonant your soloing is intended to be.
The first peculiarity for me is that while plain augmented triads, and less rarely, augmented major seventh chords are used in jazz, the most common variety of chords with augmented 5ths found are dominant (flatted) sevenths.
The second peculiarity is that Russell has a chromatic progression in the scale between the C♮ and D♮. I assume that he intended this scale to sound 'bluesy'.
Since most augmented chords are also dominant 7ths, and that contiguous chromatic notes tend to "stick out", a more practical scale for dominants with raised 5ths might be the ascending melodic minor beginning from the 4th degree.
This contains the root, major 3rd, augmented 5th and flatted 7th, without any contiguous successions of minor 2nds.
C D Eb F G A B C D E♭ F G A B C
Another alternative to the F major augmented fifth scale is a whole tone scale starting from F.
The lydian flat seventh scale.
F (G) Ab A Bb B C D Eb (E)
As others have correctly pointed out, Russell is just listing the most commonly used tones played to create a 'blues' sound.