Is it bad form to ask a tattoo artist to use art that isn't theirs (e.g. sketches by Picasso, a famous painting, etc.)?
It depends, I think, although an individual artist might disagree.
Getting a tattoo of a famous painting (like Salvador Dali which is en vogue) makes it a tribute to something well known. But getting art off like Tumblr or DeviantArt is like picking pre-made flash and asking your artist to be a photo copier.
But, if you really like something you see online, print it out and bring it to an artist who’s style you like. Have them help you make it your own, original piece.