I'm not sure if anyone here would know the answer to this, I do I know I have no idea.
Your best bet will be to submit a support ticket to them directly and ask if the messages are stored encrypted or not.
https://support.fongo.com/hc/en-us/requests/newThey are for sure on the phone somewhere as I can read my messages when not connected to any network. If they are on your phone then the data can surely be got if someone really wanted to. The question then really is if it is encrypted to the point where they can't read it unless they use the app itself. This you will have to ask the developers about, but I'm not sure how much luck you will get there.
I would be interested in knowing what they say, if you do manage to get an answer.