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This item causes the move Techno Blast to become Fire-type. It does not change it in any other way, however, and has no effect on a Pokemon without this move.
Only two Pokemon in the game can use Techno Blast, and the only one who can actually make use of it is Genesect. However, you really shouldn't be using this item even on Genesect, for a number of reasons. For one thing, holding Burn Drive means that Genesect cannot then hold a boosting item, and will miss the kick from Life Orb or Choice Scarf dreadfully. Furthermore, Genesect has access to Flamethrower, which is more powerful than Fire-type Techno Blast regardless, and does allow you to use Life Orb. Like the other Drive items, you should never use Burn Drive competitively. It is just not worth it.
The Burn Drive is received in Pokemon Black if you show Genesect to the Scientist inside the P2 Laboratory on Route 17. It is not obtainable in Pokemon White.