Since bran is milled from the grain itself (whether from the rice, oats etc), I'd be really cautious - especially bc Megan's system is really fighting for balance right now...you wouldn't want to give her anything that could cause even a small change to her already vulnerable immune system.
However, for confirmation...maybe ask your Vet Derm's tech to ask the Vet Derm. Or, if working w/ your general vet, your general vet could call for a quick phone consult w/ a vet derm.
I'm not a big fan of Missing Link bc it has flax (another iffy thing for allergy dogs), barley, bran, nuts --- which all could be sensitive for Megan right now.
Are you planning to homecook for a good while? If yes, then I'd definitely consult a Vet Nutritionist for specific supplementation - it can be really tricky and delicate for an allergy dog...and if she gets out of balance, she could develop even more allergies. This is a good one:
https://secure.balanceit.com/
I do like this general supplement...but again, it'd be so helpful to get a professional opinion:
Nature's Farmacy - Store - Product Details