Yes, eggPlant can be used to automate a Flex application. eggPlant is neither object- nor coordinate-based, but instead uses images to drive any user interface as a human would. This technology-agnostic approach allows you to test anything from Flex to Silverlight.
I highly recommend contacting email@example.com and arranging for a demonstration of eggPlant in action. In the meantime, I recommend having a look at http://www.testplant.com/community/testtube. There are several examples of eggPlant performing various tests. Anything you see here is applicable to testing a Flex Application.