I've coded Flex websites and regular Javascript/HTML websites with CodeIgniter. If you're using Flex almost exclusively, you don't have to worry (as much) about the views side of CI, but you can still utilize the controller/model setup. In your Flex app, just send JSON-encoded strings to CI controllers, and have the controllers send JSON-encoded strings back. There's nothing inherently wrong with doing it this way. I've heard things about how AMFPHP is "easier" to use with Flex, but I've always taken this as Adobe fluff. If one day you want your app not to use Flash, you will be doing yourself a favor by focusing on JSON instead.
Regarding Zend vs. CodeIgniter...that's a complex topic. Whenever I've looked at Zend, I found it to be a bit more annoyingly verbose than CI, and I've always thought CI really does MVC right. Alternatively, you can take a look at Kohana, which uses an HMVC framework. Regardless, how all of these connect to Flex in particular, I think that's a fairly straightforward issue. We're talking about HTTP requests and how to encode them. If you're comfortable with JSON (and in PHP, it's really impossible not to be), this shouldn't really be a point of contention.