Just like using a Google font for the front end of your site, you have to load the font definition and refer to it in order for the font to be used. The editor is not looking at the fonts on your computer, so it does not pick it up. And the theme is not loading that font on the front end or referring to it, so it will not be used.
To use it in some posts, you can make a special function in your theme or a plugin, to load the font on certain pages and refer to the font in the CSS. Or you can load it in all pages, and only refer to it on the ones that use it.
To load it, you will need to have a font kit which consists of the font in 3 or 4 formats and the CSS to refer to them correctly. Take the font file you have over to Font Squirrel and upload it. It will generate the kit for you to download. Put the font files in a folder on your site, such as wp-content/uploads/fonts or if you have a child theme, put them under that. Then you change the CSS that came in the kit to point to the folder you put them in. Then put that CSS into your child theme style.css or in the Customizer under Additional CSS. This can be confusing since the url() in CSS is relative to the stylesheet, so if you use the complete URL to the font files, that is best. But this is only good for the front end. To get the font to show in the editor, you will need some PHP to call add_editor_style() with that CSS to not only load the font, but to apply it. The application part is to determine the part of the content that you want that font used for. You can mark it in the content with a class name like this:
<div class="burmese-font">
<p>several paragraphs of Burmese stuff</p>
</div>
and your CSS would have
.burmese-font { font-family: "Burmese Font Name", "fallback font","other fallback"; }
