A guess? look at the equations.
In the same volume of air say, you need twice as many cyclohexenes as you do cyclohexanes to combust. So cyclohexanes will more readily combust.
What do you mean? the mole ratio is 1:9 and 1:8.5, they're pretty similar.
Similar yeah, but it facilitates a direct 1:2 ratio because you can't have a fraction of a molecule.
Ah, but it doesn't, because the equation describes a mole ratio. It's true to say that 1 molecule of cyclohexene cannot react with 8.5 molecules of dioxygen, because it's impossible to have half a molecule, but 1 mole of cyclohexene reacts with 8.5 moles of dioxygen, which is perfectly reasonable. So the increase in volume is less than 10%, which doesn't matter that much.
The double bond is more reactive and a single bond, but I can't give a good answer as to why the flame is smaller (intermediates of the reaction) and why the time is shorter (reaction kinetics). I'll probably pin it down to the stability of the two molecules, and conclude reactivity of the double bond is greater, thus faster reaction. As for the size of the flame, that's probably with how much cyclohexane you used and whether it was spread out or not.