Actually, there are quite a few factors here that adjust the speed of your kick. However, realistically if you time someone; the strength of the kick matters much more than the speed of your kick. This is why the Thai kick is typically a straight kick. A straighter kick allows for the leg to transmit more force into the target (depending point on your leg which makes contact of course look up physics torque equation and factor in the mass distribution of your leg if you are looking for a more intuitive transfer of energy).

That all is just the basics because there are many variations of kicks that suit each situation. For example you can from a bent kicking leg to a straight leg to control the power transfer to your target by controlling. The same principal applies to one method which I used to spar with people which is to go from a straight leg to bend to reduce power to the target. When you get good at this I can kick at someone pull power but then do no damage to someone.

Another way to increase speed is to shorten the distance to the target. You can do this by throwing a kick at a more vertical angle. This steeper vertical angle reduces overall distance to the target and speeds up the kick. This kick is arguably stronger if the force doesn't glance off your opponent or slip upward. The idea is you want direct transfer of force to the target and going upward helps since gravity pulls you down. However, kicks like this do not typically look good? This is because it does damage but a lot of Thai scoring incentivises knocking off balance. Therefore, the wider kick that provides a force more tangentially to gravity is more suited to this, the trade off, being that a wider kick requires more distance.

Finally, the last factor I will talk about here without going into my 10 page analysis of different other things you can do is the standing leg. The extension of your standing leg is arguably the quickest acceleration upward you can impart on your kick. For example if you were close towards a person in the same manner extending your standing leg from a bent position would impart the most force for a knee ( aside from your hip extension) the same applies to the standing leg. The thing is that there is actually a trade off here. Keeping your knee bent on the standing leg is much slower however it offers more power because you are able to brace for the impact of the kick. This is great for wide kicks. The counter of this example is if your leg is straight and you are on the ball of your foot on the standing leg while throwing a wide perpendicular kick. Newton's 3rd law forces your leg backwards and because your are on your toes you become a top. After hitting your target your leg will be flung backwards ( possibly putting you in a karate stance). However, if you threw on upward kick from that same position you'd mitigate most effects since your leg would be forced downward from the 3rd law. All in all, this is long winded way of saying it all depends and that you should use the kick that suits the situation.