What State of Matter is Fire?

No, water isn't wet. 

The is water wet? question suggests a misunderstanding of a word in chemistry. A single thing cannot be wet. A liquid will cover a surface better or worse than a different liquid. The better a liquid covers a surface, the better that liquid is at 'wetting' the surface.

It's like asking what your tongue tastes like. It doesn't taste. It tastes.

So, what state of matter is fire?

I like the analogy that Hank uses at 1:05 - what state of matter is a waterfall - works nicely for me. "A waterfall is a process caused by a bunch of liquid and gas and solids in a specific situation. ... A waterfall isn't matter because it's a process."

Fire then is also a process of fuel and oxygen reacting to form other chemicals (mostly carbon dioxide and water).

Fire is not matter, and Hank says that pretty well.