Fire is much more complex than that. Fires appearance comes from:

• blackbody radiation, as you point out from smoke particles but also from gaseous components
• chemiluminescence, the chemical reaction itself emits light, and this is why fires can burn in different colors. In fact you can buy additives which are generally metals which make fires burn blue or green or red, etc.

Fire is an active chemical reaction. It's a transition between often solid or liquid, sometimes gaseous, fuels, into gaseous products, all while undergoing a chemical reaction. It's not a state of matter, states of matter concern the phase of equilibrium conditions, and fire is decidedly not in equilibrium.