The question makes little sense, really, because it all depends on your mobile application and because you did not formulate requirements and did not explain any particular problem.
Well, for formatted text, you can use HTML or XML using HTML markup, just to save time on inventing something on your own. But HTML along will not be enough, because you would need to send images. Images are not sent in HTML, they are sent separately, through URLs and separate HTTP requests, but you would need to pack images with your data. Images should be binary data (except vector images, which can be embedded using SVG or XAML, XML-based formats; but I suspect you mean pixel images). So you have to create a format on top of XML, to combine it with XML and/or HTML.
One such format already exists: e-mail message format. The images are packed as separate
parts which you can reference inside the mail message using special
URL scheme "cid:". Please see my past answer:
Sending HTML attachment with images[
^].
The only problem with mail message format is that images (and many other kind of parts using different MIME types) use base-64 format over the binary, which takes more space (this was done because mail message format is based on pure text). So you can think of something else, with less complexity than mail message format, but you could binary format for images.
Besides, you need to develop some
application-layer protocol and implement it on both sides. It can be implemented on top of TCP and the implementation can use Java sockets. You can also use, for example, FTP. Please see:
https://en.wikipedia.org/wiki/Application_layer[
^],
https://docs.oracle.com/javase/tutorial/networking/sockets[
^].
—SA
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