You can pursue a career in anything if you have the skill to market what you are trying to pursue. Note, I said skill in marketing, not kickboxing or fencing. You can make it into something new, like MMA is marketed as the 'new' and 'better' martial art when it is not and merely took things from many traditional martial arts, threw it all in one pot, stirred it and served it. It's all how you package it.
You can make a career on those subjects writing books about it, make it a health exercise and you don't even need a lot of Kickboxing or fencing skills to do that as long as you have the skill to motivate people to want to do it and convince them that they will be healthier if they do.
Even if you would want to compete in kickboxing and make it a career that way it still takes marketing skills, being at the right place at the right time and taking the right opportunities and knowing the difference.
You could become a teacher in either and then it takes marketing and people skill to attract students. You could try and sell it to big companies telling them that you will teach at their place and that their employees will be healthier and miss less work if they do what you teach. It's all about how you can sell it.
If you want to make any sort of money in martial arts or fighting you are more or less limited to boxing or mma. There are other ways. Like Liondancer mentioned you can teach, open a dojo/gym and so on.
I don't think there is a professional kickboxing league but I know many mma fighters that come from a boxing/wrestling background, also fencing is more of a European sport.
I think that is possible, it depends on your efforts.
If not, what about fencing?
