Does this work? :

Tommen: Kneel Tommen to draw a card. + 'Flogged and chained'

My only doubt is that 'Kneel Tommen' is a cost, and I'm not sure if that qualifies to trigger the flogged and chained ability.

Also, it's my understanding that in a situation where two effects would trigger at the same time, the 'first player' chooses the order.

So, in the case of Varys 'After Varys comes out of the shadows, choose and discard 1 ally character from play, vrs. Margery's ability, when a card comes out of the shadows, choose a non-lady character... Treat that character as if it's text box were blank.

Would Margery be able to stop Varys' effect from resolving by making his text box blank? The way we played it out, Margery's owner was 'first player' and chose to resolve Margery's effect before Varys'

Tommen isn't knelt by a triggered effect, he simply pays the cost of a triggered effect by kneeling. There is a difference between the two. Kneeling Tommen to use his ability would not trigger Flogged and Chained.

Varys' ability would happen first, regardless of who's first player. His ability is passive (There is no bold text such as Response: before his ability, which would indicate a triggered effect), so it MUST happen immediately after he is taken out of the Shadows unless there was some pre-existing effect that would otherwise prevent it (i.e. An imaginary plot that says "When a card comes out of the Shadows, its text box is considered to be blank, except for Traits.)