The first lighter was produced in 1816 by a German chemist named Johann Wolfgang Döbereiner. "Döbereiner's lamp," as it was called, was a (highly dangerous) cartridge filled with hydrogen and triggered by a platinum catalyst. Lighters didn't really start to take off until Zippo began mass producing more practical models in the 1930s.
Match-like chemical reactions began back in the 17th century with the discovery of phosphorus, but the true friction match was not invented until 1827. In that year, a British chemist by the name of John Walker made matches out of long sticks with a combination of antimony sulfide, potassium chlorate, gum, and starch on the end. He called his invention the "Congreves."