My strong guess is the oils...at least one of them. Although, I would have expected the doxy to be counteracting the acne flare-ups. The action of the doxy is to help keep oil flowing, thus preventing the acne-like buildup of oil that ultimately results in a blemish.
It doesn't to me you are overdoing the oil...maybe just a bit. Consider cutting one of the out to see if things improve. If nothing does, but out the other. Experiment until you figure it out. You may be able to continue with both, but may do better just to decrease them both a bit.
Because you are taking the doxy, I'm still cannot help but consider you may be allergic to one of the oils. I would guess the fish oil to be more allergenic than the flaxseed, but I'm no expert.
I did experience a breakout while I was taking an oil supplement every day. Can't say what kind it was and how much I was taking. My skin was more oily as well.
Experiment for a while and let us know how it turns out.
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