According to Nuance Dragon 6.0.8 is compatible with High Sierra. But in High Sierra the ‘scratch that’ command doesn’t work. The correction window doesn’t work either. These are pretty crucial to an everyday user of Dragon. So unless you absolutely need to be running High Sierra, I’d suggest you stick with Sierra and run Dragon 6.0.7 until those issues are resolved.
UPDATE 2/2/2018: See this post for a fix to this bug.