This would be an interesting business indeed. You need to be careful with laws in varying states however. The reason why you are always warned that there may be someone recording or monitoring your call for "training purposes" is most states require both parties know that a recording device is in use. When starting up a three way call you need to disclose that there is a third party that is listening in on the call.

However using the same line for "training purposes" is actually a great way to do it. Something else you can do is use Google voice since it will record your phone calls for you. The catch is they have to call you for Google to record the call (again this is for legal purposes) but all you will have to do is press 4 and they will record the whole thing.

In this kind of a business you can easily have your client call you and then you call the prospect so you can record the call. Just make sure that the client alerts the prospect that the call "may be monitored for training purposes" which is completely true in your case.

As far as marketing goes I think a great place to start would be to find small business owners who use cold calling as a way of getting new clients. Then I would create a package where you monitor X number of calls and then go to their office or a skype call or Google Hangout or something and train them on how to do better. I would also suggest having written material they can keep as well. You have a fantastic idea!

Let me know if you need any help in marketing or setting up the business.