Question

Will Brick Break break the whole team's Reflect or only the Pokemon which takes damage?

Answer 1

Brick Break will break's the whole team's reflect so from that point on, all opposing Pokemon will take the normal damage, unless reflect or lightscreen is set up again.

Answer 2

The user attacks with a swift chop. It can also break barriers, such as Light Screen and Reflect.

Yes, brick break will break the opposing team's light screen or reflect and inflict damage on the Pokemon. The effects of light screen/reflect is gone after brick break is used unless the opponent sets it up again.

However, if the opponent has a ghost type Pokemon, the brick break won't effect it and therefore, would not break reflect or light screen.
On any other Pokemon, brick break would work.

Sources: bulbepedia