The flu jab is not a live virus, so that part is definitely wrong. Isn’t there a helpline for Aubagio, the same as for most DMDs? They should certainly know what is and isn’t OK with it. Your neuro should also know.
Flu isn’t just nasty, but greatly increases the risk of relapse, so it’s good to be immunised if you possibly can, but sensible to check.
The NHS web page about the flu’ jab doesn’t list people on immuno-suppressants or immune modifiers as those who should not have it. That’s possibly not conclusive proof, as they cannot list every possible individual circumstance, but the key thing they’re concerned about is allergies: anyone who’s ever had a bad reaction to it in the past, or anyone allergic to eggs (they use egg protein to make it).