I have 5 Pokemon on my Bench, and 2 of them have the "Omega Barrier" Ancient Trait. If my opponent plays Avery and I choose the 2 Pokemon that have "Omega Barrier", do they get discarded or is the effect of Avery blocked?
Yes, they get discarded. The discard effect of Avery is on you, the player choosing the Pokemon, not on the Pokemon with Omega Barrier.
Source: TPCi Rules Team (2022-01-20)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH6_130
SWSH6_130