Most times when we train against kicks in our dojo it's against mae geri (front kick). When I do demos I throw in a few responses to roundhouse, spinning back hook, side kick etc. as long as I have one of my TKD or Karate students.
In my experience, Sen timing and strong entering techniques (irimi nage and other atemi waza) tend to handle the majority of kicks pretty easily. I personally view combos (as done in TKD) as a string of single attacks, the key is to enter on the first and eliminate the possibility of the follow ups, otherwise, timing and ma ai control is critical to utilise the gap between combo kicks to create an opportunity for technique.
Generally we do not train against high kicks very often, merely because most folks are not able to execute the high kicks well and with control and more importantly, the higher the kick the higher and harder the ukemi as the body is supported by only one foot and is VERY easy to throw. In a class of relative beginners this may compromise the safety factor. In my experience everyone who has received a medium force Aikido technique from a high kick has had at least a minor whiplash effect on their neck (from the sheer shock with the ground) after ushiro ukemi, and this is from folks who have pretty solid ukemi experience. It is becoming a more regular element of our practice though as people's kicking skills are improved, and entering against a front kick (or chamber) is a part of the basics of every class during exercises like Gassho Uke, Seichusen no Bogyo and even Tai Sabaki practice.
Just my 2 cents.