Dedicate each designer exclusively to one particular scrum team. They should feel like they are a part of their scrum team and feel connected to that team’s focus. In doing so, the designer’s priorities become clear. Their priorities are synonymous with the team’s, thus enabling them to clearly understand where to expend their energy.

I am completely in favor of dedicated UX folks on an agile team. This breaks dependencies and gives a greater sense of team.

If you are a kanban shop, I suggest adding two queues to the front of your board: "In Design" and 'Ready for Dev".

Also, remember that UX is not graphic design or even information architecture. The work has some overlap, but user experience design involves a lot of thinking, prototyping, and testing.

Don't try to shortcut UX work, or you will get bad results.