Of course you want light reflected off of the background coming into your lens, that's the whole point in order to get a seamless white background. Setup your subject lighting, and then throw a strobe or two in the background, usually at higher power than your subject, and make sure it gives you the white seamless you are looking for.
Lens flare is usually light entering from the edge of the lens and bouncing around inside and causing the haze and/or flare. If you have a hood on, and you aren't pointing the lens with a light source near the edge of the field of view (which is what the lens hood is supposed to help avoid), then with most lenses you should have little to no flare or haze.
So, if you are adding a rimlight or some lighting directly behind/to the side of the subject, you may encounter a situation where you might flare or haze. This is why you always check your setup, and if you shift position/angles double check after the first shot or two to make sure you're good.