I've never found a scrub / exfoliator that doesn't break me out! Including homemade ones with sugar or salt - they're too harsh / rough / sharp for my skin.
A couple of times while on the regimen I've used a face towel to really gently exfoliate after cleansing at night and this has worked well enough for me. Not great though. But helps with the flakes a bit (though you know what it's like, trying to remove flakes is an endless process and you can just end up disturbing / creating more flakes if that makes sense) and it doesn't seem to break me out.
You can also use jojoba oil to exfoliate which might be a better idea because it's probably more gentle and creating less irritation than the face towel (even though I'm gentle with it) - so try the jojoba oil exfoliation method first! I think I'll go back to trying this one too actually...
You take a fair amount of jojoba oil and put this all over your skin, let it sit for a couple minutes and then start gently rubbing your face in circles and it should start removing flakes - then cleanse face as normal.
AHA is supposed to be good for flakes too.
I knw this may cause a lot of irritation but I use packing tape to pull all the yucky skin off and it works better than any stupid dermabrasion I have ever tried. Just be gentle. I get a few zits here and there but because of harmons I think. I also use baking soda and water and do scrub it and I don't seem tot break out because of that Ive been on regimen for 7 mo!
I've never had an issue exfoliating even on the regimen. I use the St. Ives Apricot scrub. I do it twice a week on the mornings after I have a full face of AHA at night. I feel like it really helps get rid of any BP and dead skin cell build up. I do it very gently and no more than a minute. After the scrub, I then wash my face with my cleanser to get rid of any left over scrub bits and wash of the salacylic acid so it isn't too drying.
I have been using the jojoba exfoliating method followed by the Acne.org cleanser. You put about a teaspoon of oil on your face, massage lightly for a few minutes, leave the oil on like a mask for about 10 minutes, and then cleanse as normal (10 seconds). The oil and friction lift the flakes you may have, but it is super gentle. I do this a couple of times a week in the morning because I don't have any makeup on and it leaves a smooth surface for my makeup. It has worked wonders on the flakes.
I also use the AHA+ every night after my BP. I use about 1 pump of AHA+, let it absorb for 15 minutes, then use 1 pump of the Acne.org moisturizer + 10 drops of jojoba oil.
Don't use a scrub, it can tear the skin and invite in more bacteria. The nice thing about the AHA+ and jojoba oil is that they draw more moisture into the skin.