Most defiantly you can still get lens flair while using a lens hood - the collapsible reflector is very good and as I said before - I always wear a hat not to just shade my head but to shade my lens too when needed.
f4frank wrote:
The official name is "lens flair", it occurs when the incoming light refracts on the lens elements.
Those who suggested a lens hood are correct.
Most photo stores also sell a 12" or 14" reflector that folds up to about 3 inches. Its extremely lightweight and it can be use to shade the lens in those flair situations. Even with a lens hood you might get flair.