I have experienced the 50% for working for an employee (at the beginning, clients were assigned, but through experience most were referrals). In addition, I have worked for others where I have taught classes, and if I bring in my own clients to train, then I would pay from 15-20%.
These days, there are more and more gyms and small studios opening up, and those people have to pay overhead. So, many are looking for trainers to come in and you may find a few different places to train depending on your clientele and their needs.
If you go the flat fee route, just make sure you have enough clients to support the cost.
Best wishes to you–and always try negotiating to your benefit!