Oh man, I totally did this last year. I had a pile of flagstone and swore it was basalt. A buddy made me do the scratch test with a nail, and slate flaked right off. That hardness check is a solid way to tell, in my experience.
Yeah, those fine lines are a dead giveaway for slate. My friend was so sure her patio stones were basalt until she tried the nail test. She pressed a nail into one, and it flaked apart in layers, just like you said, @the_dylan. Now she double-checks every stone before buying.