> Who prioritizes?
The same people that did before.
> Kanban seems very chaotic
Business is very chaotic. Admittedly, we (where I work) are a very bare-bones team, so we are quicker on our feet than a larger organization.
The main issue we would run into with "sprints" was that the business world-view didn't stay fixed for 2 weeks at a time. There was always something that came up and got bumped in priority. This led to people feeling disappointed that "we blew the sprint".
In reality, "the sprint" doesn't matter. Solving business problems matters. Kanban (Wikipedia says it's just japanese for "billboard" i.e. "big priority board") is just a way of explicitly stating the current priorities so that you can react to them.
> As a manager, how do I know how long a task should take?
You still break down big tasks into small tasks and estimate them. The planning process isn't really any different than with sprints, it's just that you're more free to make trade-offs in real time.