How does his immunity works with this (immune to trigger abilities)??? Is he immune to gaining the keywords or immune to being chosen??

Yes. Pretty straightforward, really. Banner Bearer has a triggered effect. Joffrey is immune to triggered effects. Therefore, the effect on Banner Bearer cannot work on Joffrey at all.

For more detail, though, Joffrey's immunity to triggered effects means he:

1. Cannot be "chosen" as the target of triggered effects.
2. Ignores the effects of all triggered effects that would be applied directly to him, whether they target him or not.

Banner Bearer has a triggered effect that both targets a character and affects that targeted character directly by making it gain keywords. So it fails to on both #1 and #2. About all you can do with Banner Bearer and Joffrey is put it on Joffrey and use it to make a Lord or Knight immune to triggered effects.

ktom said:

This is not what the banner does though xD.

Text:
Condition Setup. Challenges: Kneel Banner Bearer to choose a Knight or Lord character you control. Attached character gains all keywords the chosen character has until the end of the phase

So if you put it on Joffrey, you'd have to select another Knight or Lord and joffrey would gain the keyword(s).

So you have 2 possibilities, that by your response I'm assuming both would be invalid.

1. Put it on another character and choose Joffrey (lord) to give that char (the one with the banner attached) immune to trigger effects.

2. Put it on Joffrey and choose another Lord or Knight to give joffrey (without actualy selecting him) to give him the keywords the other lord or knight has.

Francisco G. said:

But yes, your interpretation is correct. If you put the attachment on someone else, they won't be able to get Joffrey's immunity because of #1. If you put the attachment on Joffrey, he'll get nothing because of #2.