How To Get Dratini in Pokémon FireRed/LeafGreen Version
Note: You must obtain the Super Rod in order to locate Dratini, which can be found in Route 12. (The Route below Lavender Town).
It is a 15% chance to find Dratini with the Super Rod, so be patient!
Also: Dratini can be found in the Celadon Game Corner as well, it will be at Level 18 and will cost 2800 Pokédollars.