I have the same type of skin (tho mine also gets dry flakes/ patches in the fall/ winter, with oily skin underneath, if that makes sense -- it just started happening 3 or so years ago).
The best thing I have found is the oil cleansing method. It sucks all my black heads out, softens my skin, and makes it look less red and inflamed.
However, I do a few things differently: I'm using a massage oil blend that has lavender and chamomile EO in it (base oil is almond). Those are good for sensitive skin, which I also have. I use a LOT of oil, and massage it into my skin for a long time (the longer the better, really... up to ten minutes). I'm not too rough, but I do feel a lot of junk come out when I massage.
Then I do the steam with a washcloth, like they recommend and then wipe off the oil. Sometimes, tho, I also wash my face quickly with my foaming Dr Bronner's. It depends on how my face feels.
If I was being very good to my skin, I would do the OCM every night, and wash with just warm water in the morning. However, I'm not that disciplined, and I would say I mostly wash with water. That's better for my skin than any cleanser I've ever found. Of course, I still have some breakouts when I do that... but not nearly as bad as when I was using a TTO cleanser and scrub.
(Obviously I don't wear makeup -- if I do wear makeup, I wash with OCM or Dr B's).
I know it is a BIG leap to make for an oily skin person to try using the oil cleansing method. But I looked at it as a grand experiment. What was the worst that could happen? My face would break out? Yeah, what's new?
(My secret breakout buster is Vit E oil. It seems counter intuitive, but my gosh that stuff really works! I had red acne scars on the sides of my forhead that hadn't cleared up in months when I started using the OCM and putting Vit E oil on blemishes. They're mostly gone now! I consider that nothing short of miraculous...)