HTML styles are automatically stored in a your local site's Library folder in a file named Styles.xml.

The good news is, you can copy the Styles.xml file from the Library folder of one local site to the Library folder of another local site and reuse styles you created.

The bad news is, each site can only contain one Styles.xml file, therefore, if you created new HTML styles in the site to which you are copying a Styles.xml file, the file you copy there will replace the existing file. You won't lose any formatting changes you've already applied, and you can recreate the styles by selecting text in the document and define a new HTML style.