Lens shade should reduce flare, as long as it doesn't darken the corner, right?
I found some bright flare or ghost edges in some of my pictures. These were taken with a long long shade that I borrowed from a friend.
For investigation, I looked through the lens when it's off the camera. Interestingly, I saw the reflection of inner surface of the hood, Although there's no sign of corner darkening in the picture.
With the shade off the lens, the picture is better.