Are vascular conditions a common complication of inflammation?

Yes: Almost all disease states have inflammation as a component. Now some micro-vascular autoimmune diseases are a direct result of an inflammatory process. I need more specifics of type of inflammation you are referring to.

PAD/inflammation: PAD or artery disease is plaque. The plaque grows until a vascular event occurs, (stroke, heart attack, limb loss). The risk factors driving plaque growth are hypertension, high cholesterol, diabetes, and nicotine addiction. Inflammation is not a major driver/risk factor contributing to PAD, however many vascular patients also have arthritis inflammation.