Can you kneel ANY character with an Intrigue icon? Or just your own?

Just your own character.

From the Rules Reference "Costs" section (page 5):

Some card abilities are presented in a “do X to do Y” construct. In such a construct, the “do X” aspect (preceding the word “to”) is a cost, and the “do Y” aspect (following the word “to”) is an effect. An opponent’s game elements may not be used to pay a cost.

When I thought about usage, logically you would have to use it with some low cost, single INT icon character. Like Lannisport Moneylender to boost his income. Or Queen's Assasin after you already ambushed him, he's not much use. Same goes for the Red Keep Spy. From neutral characters there is Wildling Scout as a good candidate, you can still sacrifice him later for stealth.

Or you can use it with NW banner, and then the Steward at the Wall would provide 1 gold, instead just decreasing the cost of NW cards.

Another way how to look at the Chataya's Brothel is as reducing a cost of some claim soak. You marshall a character with INT icon you know will die in Challenges phase as a claim soak. Chataya's Brothel will make it 1 gold cheaper.

Also there's a possibility to combine it with the "Small Council" members, like Littlefinger, Varys or LoCR Tywin and then use the The Council Consents event to stand those characters. However this combo is too clunky as The Council Consents is triggered only after you win an INT challenge by 5...

Possibly the most effective times to use this card would be in the taxation phase of the turn prior to playing either First Snows, Valar, or Wildfire Assault. You likely knelt the characters during the challenge phase, though and this situation is so specific that you've likely got better/easier ways to make money.

Possibly the most effective times to use this card would be in the taxation phase of the turn prior to playing either First Snows, Valar, or Wildfire Assault. You likely knelt the characters during the challenge phase, though and this situation is so specific that you've likely got better/easier ways to make money.

I don't think you can use it in the Taxation phase. Card says: Marshaling action. If it would be possible to use in the Taxation it would be a great card. Now it's almost unusable...

Pfft! It's currently being voted as one of the worst card of the cycle, why would I bother *reading* it?

Yeah, this card would be weak even with a cost of zero. The thing is that I usually try to focus on such bad cards because I always think that I'm missing something. It's a good brain exercise.

I was also thinking about the Mountains of the Moon location and Clansman trait, as such character could be marshaled and given INT icon to use Brothel. But the price of kneeling even weenie character is too high in my opinion. Brothel should give gold based on number of challenge icons like the Crown of Golden Roses (which gives +STR).

I like the irony that the best characters to use with this card are so far Citadel Novice and Satin (sworn brother).

I think this location needs some other cards to be of any use. F.e. some Lanni character attachment which gives you 1 gold when you kneel attached character.