"There's already a node about this" at the messed-up meaning of inflammable, but I think they should all be moved here. If someone was actually confused about what "inflammable" did or should mean, this is where they'd look. Oh, I'm a god now, I can move write-ups. Flame On!
The long-standing English word for "capable of going up in flames" is inflammable. It comes from the same root as enflame and inflame, where the Latin in- means the English in, as in in flames.
In Latin there are two different prefixes in-, the one meaning "in", and the negative one (related to English un-). So the word inflammable looks (falsely) like it's the opposite of a word flammable.
But the word flammable is effectively a recent invention. Although flammability is recorded from the seventeenth century (in that great word-coiner Sir Thomas Browne, who however also used inflammability with the same meaning), it never caught on. Never took fire, so to speak. Webster 1913 briefly notes it and marks it [Obs.] (obsolete). The OED has quotes from 1813 and 1867, then the next one is 1959: it's from the BSI (British Standards Institute), suggesting the adoption of the word flammable for safety reasons, in place of inflammable.
Likewise, flammability has two sporadic quotations in the seventeenth century, but next appears in 1942, and in 1963 the BSI again call for the word flammability to be adopted in place of its dangerous synonym inflammability.
And what if something couldn't catch flame? What did we used to call it? Non-inflammable.