If the sun doesn’t burn what are all those flames shooting out of it?

Those "flames" are properly called solar prominences, and are found associated with sunspots and flares.  The Sun produces energy through fusion of hydrogen atoms into helium.  This happens only in the solar core, as incredible pressure and heat is required.  This was discovered by a University of Michigan astronomer named Subramanyan Chandrasekhar around 1950, and got him a Nobel Prize, plus the Chandra Space Telescope is named for him.

After a fusion occurs at the core of the sun where 4 protons yield a helium nucleus, the energy released takes tens of thousands of years, sometimes one million, to reach the surface of the sun through what is called the convection zone. The flares are due to the magnetic fields in the sun and are composed of energy and plasma and have loop forms. These loops could "burst" and send solar winds into space. They look like a burning fire in some way, but they are not,

Not flames.  Gaseous matter (or really, at least in part, beyond gaseous, a plasma) at extreme temperatures.  Way hotter than "flames".  Heat is not fire, although fire does emit some heat.

The sun is not fire in the terrestrial sense.

The "flames" are called "solar flares" and what looks like fire is superheated plasma.

They are Outbursts of Solar Plasma

From what is a vast uncontained Nuclear Furnace

Only contained by its own Gravity

Those flames are nuclear fusion. Hydrogen is being converted into helium, just like in an H bomb. 

Not Flames.  Plasma from Nuclear Fusion.

Gaseous plasma.

You’ve got the IQ of a block of wood.