Excellent question. To my knowledge there is no equivalent function in epub. In a web browser, RTA is done on the meta tag in your browser. But with epubs, you already have to store your Dublin Core metadata in the package.opf file, so there is no need to do so on individual html files.
I skimmed the Dublin Core metadata and did not see anything for an Adult label, although perhaps genre/audience/subject might be relevant here.
I knew that when you sell your ebook, Amazon or Google Play ask you to put a put it in a category (I later learned that they correspond to BISAC codes). An Oreilly article mentions other categorization schemes like marc and onix.
To summarize: The book creator usually can mention certain DC values which will be wrapped up in the epub. But I don't know of ebook reading systems which are using it to prevent the user from viewing it. On the other hand, when you submit your ebook to an ebookstore, they usually ask you to give some values that would allow the store to prevent younger readers from seeing it or buying it.
But what if you are selling directly from your own website? What can you do? In addition to RTA labeling, you can require some proof of age to access the page or file. Ultimately though, when you are dealing with DRM-free ebook files, there is nothing preventing an underage user from loading it into an ebook reading system.