From a chat with @scissorscitygirl.
Omega wally being constantly horny could mean he overproduces slick instead? Like Kori could plug him up and practically drink it like wine. Maybe she keeps him plugged up to keep his uniform and clothing clean. He's only emptied if Kori or Dick allow it.
If we're going with an intersex design for omegaverse, maybe Kori has them fuck each other to entertain her and earn her cock. Omega cocks are tiny and pitiful, not satisfying for an omega at all unless they have a lot of practice. It leaves them desperate and begging for her to help them cum.
When she finally penetrates Wally she orders Dick to stay in their with her. Dick loves the feeling of his tiny omega cock getting crushed by Kori's knot. Dick only gets to cum once a day. A subconscious command engraved in his mind by her pheromones. He loves the feeling of being denied until his mistress finally blesses him with the order.