Why does a flame of the …

Flame is basically packet of hot gases. It is visible to us because of its temperature. Consider a kerosene burner, a hydrocarbon is burning and producing co2, water and heat.

For any hydrocarbon..
CxH2y  + (x+1/2y) O2 ---> x CO2 + y H2O  + HEAT

Now this heat of combustion heats the surrounding gas. This gas may have temperature varying from 200 to 1500 deg. C

Now these heated gases are around burning location (reaction location eg, candle tip), it can go up or down??

But when gases are heated their kinetic energy increases and distance between molecules increases correspondingly,  which makes gas rare and less denser.

As this gas is lighter it will tend to go up, and denser cold surrounding air will come down to replace it. 

As flame travels up it gets diluted and temperature falls, it become invisible to our eyes.