Is it possible to implement spell check on Nintex form for sharepoint?
It seems that this has been requested on uservoice, I suggest adding a vote.
Allow SharePoint spell checking to be turned off so that built in browser/OS spell check can be used...
jQuery has a spell checker you can try and include (classic forms only). It requires an ASP.NET IIS Website to run, so you should be fine as you're using SharePoint.