How do we file our Kansas Income taxes if we file our Federal taxes as a 'Qualified Joint Venture'?

It depends on how you set up your business entity. If you are running the business as a sole propriator, it goes on a schedule C, if you are running it as a partnership, then it would not go on a schedule C, it would go on a partnership return. If you are running it as an LLC, it can be a partnership, disregarded entity or s-corp for tax purposes. Your best bet is to sit with an attorney to discuss your business venture and help pick an entity that is right for you and set up the proper business formalities. Do it right the first time before it could cost thousands to fix down the road.