How to use flint in Breath of the Wild?

That's the intended way to use flint. I believe you must hit it with a metal weapon for it to generate a spark to light wood.

Hitting a pile of wood with any fire weapon (sword, spear... includig fire arrows) will also start a bonfire.

Where to get a fire weapon:

Top-right of the map theres a maze on an island you can reach flying. Going through one of the doors on the left will lead you to a bramble, once burned it down you can climb to a litle corridor where you will find a two-handed fire sword. There are a couple of Guardians at the start of the maze but you can easily avoid them.

I have the impression that theoretically it would be possible to start a fire with a lightning, but those come together with rain what makes impossible to set fire to anything.

Although it seems too obvious I have to say that you can light a fire bringing it from another one with a torch or a wooden weapon/arrow/shield.

As you said, flint is used to set fire, you can create your own bonfire hitting the flint with an iron weapon, light a food rack or set fire to a whole field of grass. Keep in mind that in bonfires you can still cook basic ingredients such as meat. It's also useful to make the time pass and to get warm in cold zones like high mountains or to melt ice.

Flint altogether with other materials can be used to improve some armors or forge some weapons. (Need to check this for more precise information)

There's also a guy in a horse house (sorry for the poor translation) close to the Orni town who will give you a reward in exchange for 52 flints. (Will improve this part of the answer once I can put my hands on the game)