What are the average miles per day I should be striving to achieve?

There isn't really a should. Weight loss comes down to calorie intake. The more you exercise, the more of a calorie deficit you can create (but if you want to become fit, you need to balance that with performance).
How much mileage depends on what your goals are, I mean more than just getting fit. Fit can mean a lot of different things.

15% BF is really low for a woman. Not saying don't do it, but it is quite lean. It's close to essential BF territory.

Is it a fixed gear, or a single speed (the two seem to get confused a lot)? If it's a fixed gear, it means that you can't coast, and must keep pedaling to keep moving. If that's the case, you won't be able to recover as easily on the bike because of the constant pedaling. A long race for those on a fixed gear bike (in a velodrome) is 10 miles.

If it's a single speed (only one gear, but can coast), you should be able to go a lot longer, since you are able to get that little bit of recovery when needed. Don't increase your miles too quickly, or you can risk injury or burnout.

Your knees hurting could be more about the fit of your bike than the distance/pace you are going. I'd recommend going to your local bike shop and pay for a good fitting. Especially if your goal is to become an elite rider.