Doxycycline is fine to take with the Clear + Brilliant laser treatment and there should be no reaction between the two.
In our practice, we often use doxycycline for resistant cases of acne vulgaris. We also treat these patients with topical medications, chemical peels, IPL laser, and Clear & Brilliant treatments and have gotten great overall results for our patients. I have no reason to believe there are any contraindications to Doxy with Clear & Brilliant, but your question has not been scientifically studied at this time. There is no data to definitively conclude either way. Hope this helps!