"Nonetheless" was once commonly written as "none the less." However, that that is no longer the case is indicated by the Online Etymology Dictionary, which – as @J.R. has noted in a comment – says that "none the less" was "contracted into one word from c. 1930":
Though the use of the contracted form did not immediately become universal, its use is now so widespread, and in most quarters so uncontroversial, that the older form has vanished from many dictionaries. For example, if you search for "none the less" on the Cambridge Dictionary website – using either the U.K. or the U.S. dictionary – you don't get a definition, but a page that lists words with similar spellings, beginning with "nonetheless":
Once in a while, you may find a dictionary (either online or in print) that contains a kind of "dummy" entry for "none the less" that points you to "nonetheless," like this:
In other cases, an online dictionary may automatically correct "none the less" to "nonetheless" for you, right in the search box. You can try this yourself at Merriam-Webster's site:
And I did find one online dictionary that, while using "nonetheless" as the preferred spelling, does include "none the less" as a variant – though tellingly, even in this case, both usage examples use "nonetheless":
In short, you may sometimes encounter "none the less" in print or online, especially in older sources or in modern ones that have not been rigorously edited. (And of course, the same is true for historical spellings, variant spellings, and misspellings of many other words, including compound words.) Once in a while, you may even encounter it in a source that has been rigorously edited, but by someone who has an idiosyncratic attachment to the older form. However, there is a strong consensus among educated native speakers in the present day – including the compilers of the above dictionaries and many others – that "nonetheless" is the correct or preferred form. Accordingly, if you write "none the less," it is likely that many of your readers will think you have made a mistake.