For church websites, the main reason they want to use flash is for impact. It can look really professional. However as mentioned before the main downside is accessibility.
But if all you want is fancy rotating graphics, perhaps a bit of AJAX can help?
Tim Hyde has modified one of his wordpress themes and incorporated JonDesign’s SmoothGallery. It looks fantastic and mimics the flash clickable gallery seen on many large church websites. But best of all it is fully accessible, with changing title, alt, etc. attributes for the elements.