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Flamethrower can be taught to Pokemon in Brilliant Diamond and Shining Pearl via the use of TM35.
TMs are moves that a trainer can make their Pokemon learn. Of course, the Pokemon needs to be compatible with the TM and capable of learning the move it contains.
One of the most powerful Fire-type attacks in all of Pokemon can be taught through a TM in Brilliant Diamond and Shining Pearl. You can do so by finding TM35 in Fuego Ironworks or purchasing it in Veilstone City.
Where to locate TM35 Flamethrower in Pokemon Brilliant Diamond and Shining Pearl
Fuego Ironworks
Fuego Ironworks is located north of Floaroma Town. It is just before the Eterna Forest and can be visited by using Surf while on Route 205. Surf along the stream and you'll come across the "home to molten foundries."
As you enter the building, you'll notice a furnace in the middle. In front of it lies a Poke Ball that can be picked up from the ground. That will be TM35, also known as Flamethrower. You will have to complete a spinning puzzle in order to reach it.
Once you have it, you can teach TM35 Flamethrower to a single Pokemon. The TM will break once it's used, but the Pokemon that learns it will now have a Fire-type attack that sits at 90 Power with 100% Accuracy.
Veilstone City
Veilstone City is home to a massive department store in Pokemon Brilliant Diamond and Shining Pearl. There are several floors, each filled with vendors that offer a variety of items.
On the third floor, accessible via the stairs or an elevator, you will find a merchant selling TMs. She is to the bottom left of the room with her back to the in-game camera view.
Speak with her and she will provide the list of TMs available for purchase. Find TM35 Flamethrower and spend $3000 to buy it. You can do this multiple times, which comes in handy due to the TMs breaking.
Keep in mind that $3000 is quite a bit of cash in the early stages of Pokemon Brilliant Diamond and Shining Pearl, so don't spend all of your money on TM35, unless you already have a solid plan for using for it.
