The dorian flat 2 mode and names of these scales are all related to the major scale mode names.
The dorian ♭2 mode comes rom the second note of the Melodic minor scale and can be used over minor 7th chords and dominant 7th flat 9 chords of the same root. You just have to be careful with the second note being a half step from the root.
The names of these scales can be confusing especially if you don’t know all the major scale modes.
The main thing you need to remember is a melodic minor scale is a major scale with a flatted 3rd. That is the only difference.
The important thing is do you know where the scale came from and what chords you can use it for not it’s name.
Here is a little taste of the dorian flat 2 mode played against a Dm7 chord.
The Dorian Flat 2 played against a D minor 7th chord
I’m trying to give you the overall sound that mode has. The minor 2nd interval gives it that unique quality that it has so I used this note more than usual. This note should usually be used on upbeats to avoid a minor 2nd clash with the bass note.
Dorian ♭2 Mode List
Dorian ♭2 Mode Formula
The formula is 1-♭2-♭3-4-5-6-7
It’s a dorian mode with a flatted 2nd or a major scale with a flatted 2nd and 3rd.