If there's a well established link between inflammation and cancer, why did a recent study on antihistamines say that they increase cancer risk?

No known risk. The more cell proliferations, the higher the risk that one of the proliferations may lead to a mutated cancer cell. Since inflammation leads to proliferation of tissue and blood cells, this is just a chance happening perhaps with some genetic predisposition throw in. The more often you run the red traffic light, the higher the chance that you will get hit by another car.
Junk reporting. Inflammation is itself enormously complex. Many cancers evoke inflammation, and they arise in sites of chronic inflammation (osteomyelitis sinuses, ulcerative colitis, smoker airways) if and only if cells are already being replaced way too rapidly. For "antihistamines cause cancer", i found only retrospective and mouse studies -- these make little sense ; almost never come to anything real.