I would not flush the engine but do a couple more frequent changes. A chemical flush may make that oil leak worse. Looks like the pan, try tweeking the bolts and valve cover bolts. On your C6, when you drop the pan, change that old vacuum modulator, it's only really bad if fluid leaks out the vacuum nipple but I wouldn't want that old diaphram in it to blow out in the sticks somewhere.. It's very easy when the fluid has drained and make sure to put the rod back on the new modulator. There's one "intermediate" band to adjust on a C6. Good time to do it. It's easy and you need a torque wrench and shouldn't take long. Check out those brakes and flush out the old fluid.