It can be modulating between keys, or it can be mostly in Dm. What the key "is" at each point depends on the selection and timing of the notes you play on top of the backing chords. You could make it sound like it's mostly in Dm, or you could make it sound like many other things. Here's an easy (?) Dm interpretation:
- A : D melodic minor, sounding like it might be going to Dm next
- F, Bb, Bb : D natural minor (or F major), sounding like it went to the relative major side F major (instead of Dm) at least briefly
- A : D melodic minor, sounding like it went back to the minor side again, might be going to Dm
- F : D natural minor or F major (same thing again)
- G : D dorian, sounding like the next chord might be A which would break away from the dorian sound and lead back home to Dm
- E : E mixolydian, sounding like the E is a secondary dominant heading for an A, and then back to Dm. The next repeat of the chorus with the A chord strengthens this feeling.
You might want to play an A7 chord on the second repetition of the chorus before heading back to the Dm verse, so it feels more natural.
On the G and E chords I would do a melodic variation of whatever happened on the Bb chords, complementing it in an "A-B-A-C" pattern.