I imagine it has something to do with the CO2 in the soda along with the sugars and the high heat of the wax. But why it flames up like that... I'm not sure.

If I had to guess, I'd say that this happens due to the same principle that causes grain elevators to explode from fine dust in the air. Any sufficiently flammable material, if it is in small enough particles and exposed to air, will combust. You can do it yourself by blowing a handful of flour into a candle flame. The only difference is you are generating a spray of droplets of flammable liquid, rather than flammable dust.

I can make a guess. The temp is high enough to ignite if vaporized but too low to ignite in a lower oxygen environment such as a liquid mass in the test tube, boiling or not. When dumped into the cold coke it shatters the tube and vaporizes in a similar way that grease splatters when you put something cold in a pan, carbonation couldn't be anything but a help there but I wonder if water might do also. What hits the air ignites since it's at a burn temp if it had enough air.

I'm sure someone else can explain the details better but it doesn't seem too different in principle than another I've seen, this one just approaches it in a different way and with coke instead of water. Paraffin burns well but it needs lots of air, little or no air and we get no flame. Some air and we get a low controlled flame but no dramatic burn. That's why only the wick burns on a candle but it doesn't ignite the rest of it.

http://www.madphysics.com/exp/20_foot_wax_fireball.htm

I can confirm from personal experience that this works just as well with plain old water.

I'd agree with drattus and guess that the liquid wax is shot into the air by the rapidly expanding coke, and that the wax in the air can ignite and create the fireball.

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