The fire triangle also shows us that we need heat to sustain the fire. How can we get rid of the heat? Think about putting out a camp fire - that's right - water!
When you pour water on a fire the liquid absorbs heat and is converted into steam. Absorbing heat to vaporize the water lowers the temperature and makes it harder for the fuel to burn.
When NaHCO3 is heated and decomposes to produce CO2 it also absorbs heat! With sodium bicarbonate we get two good things for the price of one - CO2 and cooling - what a deal!
However, sodium bicarbonate is not commonly used on clothing (why do you think that is?) but it works really well on grease fires in the kitchen.
A third way to keep the fuel and O2 apart is to char the surface of the burning material. The char is a complex mixture of carbon and other substances that don't burn well. If the char stays on the surface it forms a barrier to keep the O2 away from the fuel. You see some char form on the cotton ball when it burns. If we could find a way to make lots of char we could really slow down the burning process.
There are many other, and more complex, methods to make materials flame retardant - but that's another story!