There is no difference in meaning between flammable and inflammable. Both describe things that are capable of burning or easy to ignite, but in all modern varieties of English, flammable is preferred.
Inflammable, derived from the verb inflame, is the original word. But because the first syllable is easily misinterpreted as the common negative prefix in- (as in, for example, inescapable, invulnerable, inorganic), the word has always caused confusion. Because this confusion can have dangerous real-world consequences, the shift from inflammable to flammable is welcome.
The less confusing flammable did not enter common use until the early 20th century, but it quickly became the prevalent spelling. Inflammable is still common on product labels and appears from time to time in edited publications, but it fell out of favor around 1970.
This ngram graphs the use of flammable and inflammable in English-language books published from 1800 to 2000.