Hi Chris,
Image objects in Wagtail don't natively have URLs of their own, because we can't necessarily rely on editors to upload them at a web-friendly resolution - it's the job of the template to request a 'rendition' object at the required size. Usually this would be done through a template tag such as {% image self.feed_image fill-320x200 %}, but you can obtain the rendition within Python code by calling rendition = image.get_rendition('fill-320x200') - or if you do in fact want the non-resized version, image.get_rendition('original'). The URL is then available as rendition.url.
Alternatively, you could leave it up to the consumer of the API to request the image at the required size, using Wagtail's 'external image generator' feature:
http://docs.wagtail.io/en/stable/core_components/images/using_images_outside_wagtail.html
(Besides providing a user interface for generating sized images, it also provides a URL scheme for requesting them programmatically - although having said that, it appears that we haven't actually documented that scheme yet...)
- Matt