Inflammable and inflammatory can be confused with one another, but they also offer their own source of confusion with the prefix in-.

Inflammable refers to something that is easy to set on fire; something flammable. How can inflammable mean the same as flammable? True the prefix in- can mean not, as in inaccurate. But it can also be used as intensifier meaning in or into. It's that second prefix at work here. Something inflammable is something that's capable of not just being lit on fire but being easily lit on fire.

The fire created panic in the area as the spot is surrounded by dying units that produce highly inflammable chemicals.

However, we suspect that a spark in inflammable material or gas leakage might have caused the incident.

You can improvise your own personal ashtray by using an old tin of breath mints, or something similarly inflammable.

Inflammatory is also related to fire, although figuratively, and makes use of intensifier in-. Used literally, inflammatory describes something that is inflamed, that is, red, swollen, and hot. Muscle and tissue often become inflamed, and an inflammatory disease, such as arthritis, cause parts of the body to become so inflamed.

A novel treatment option for inflammatory diseases like rheumatoid arthritis seems to be underway.

Used figuratively, inflammatory describes something that incites anger or violence. It inflames people's emotions or responses.

This is false, inflammatory rhetoric.

The protestors have been known for their inflammatory remarks and signs.

The root of inflammable and inflammatory give you a clue to their meaning with the idea of fire. Inflammable is a literal fire: something that can be easily set on fire. Inflammatory is a figurative fire, whether with swollen joints or angry words.