To inflame is to make feelings stronger, or stir them up. Reminding your grandfather about the time his car was stolen may just inflame his anger.
Getting a parking ticket might inflame your frustration, and when a city imposes a curfew it may inflame the community's feelings of resentment. Another way to inflame is more literal: to cause a physical condition that involves swelling, pain, and redness. Scratching your poison ivy rash will only inflame it in the long run, even if it briefly brings relief. Inflame is from the Latin inflammare, "set on fire" and "excite."