For anyone who happens across this old post and is wondering the same, the font cannot be changed.
Phonetic letters are recognized, as well as italics and boldface aspects of fonts.
These features can be created using a dictfile (.df) and creating definitions with html code. This file can then be used as the input file in pyglossary or other scripts that use pyglossary to make a MOBI dictionary.
Instructions for creading a .df file can be found here:
https://pgaskin.net/dictutil/dictgen/#dictfile-format
When the Kindle updates, the font is often changed for the dictionary popups, however the font is updated later to the default font.