As the other answer stated, no Arcanine is not a legendary Pokemon in the sense that Mewtwo, Lugia, Rayquaza, etc. are legendary Pokemon, but its species is classified in the Pokedex as the legendary Pokemon, which could be part of what led people to this misconception. Something else that likely contributed to this misconception is, in the second episode of the Pokemon anime, Arcanine was included on a stone tablet (or something like that) on the wall of the Pokemon Center with Articuno, Zapdos, and Moltres.