Hi Axkick,
I train in Kyokushin. I can appreciate that you want to learn and compete in knockdown but depending on your age, I would highly recommend you learn how from a good Kyokushin or offshoot school. Knockdown events can range from local, regional, national and international and it is best to be part of a school that understands the type of tournament you are entering and ensure that your knowledge and skill set will appropriate for the event.
There is no problem having previous experience in Tae Kwon Do and in fact it may shorten the learning curve on some of the kicks but knockdown is not for the faint of heart and there is little to no protection other than a cup for men. I have seen a few people without a Kyokushin background enter a few local and regional tournaments but they typically did not do well. Firstly they did not understand the ruleset and more importantly they were basically fodder for more seasoned knockdown competitors.
The Sensei of the Enshin school should be able to talk to you about what is available in the area in terms of tournaments and what you will need to participate. You should be able to take a free class and if you are lucky it will be a night where there is some sparring.
If you have any questions I would be happy to answer them but essentially there is a fair bit of body conditioning you will need to do to prepare for a knockdown experience. It is more than having good cardio, it is learning how to hit and take a hit and to do that properly you need people to train with that understand what it means to compete in Knockdown.
Good luck