For anyone else with the problme, this answer is based on a response from MailChimp support:
It looks like it isn't possible to keep a custom class attached to an editable image. What you could do instead though is apply the class to the image's containing element. So if the image is in a
<div>
, addflexibleImage
to thediv
, and then update your CSS rules to point to.flexibleImage>img
.