Having your devices autographed is not that uncommon. I know CGPGray talks about doing it.
I would suggest buying a book if only because it will probably store better than a Kindle after you stop using the Kindle. I will say, though, that an autographed Kindle is pretty cool while you’re still using it. Maybe get one of each?
Joann’s and Michael’s and other craft stores have pens for all surfaces, including plastic, and the packaging will say what the pen is good for.
Paint pens are usually best for plastic, but the paint needs to be formulated to stick on smooth surfaces (plastic, glass, & metal) to be effective.
I suppose I should put my two cents in, though:
This is one of your favorite authors, right? Go buy a copy of whichever of her books you like the most and get her to sign that, maybe even along with the Kindle. It’s really nice to have a signed book on your shelf - it gives the volume a weight and a memory that can’t otherwise be replicated. When you see it on your shelf, even amid the other books, it’ll stand out to you. Nobody else will know, but you will.
It’s nice.
An analog signature with an old-tech physical pen is inappropriate for a digital revolutionary who reads only from screens.
Open a file where the author can type her name.
Not hand-signed, no.
Forgot to update this. Sarah Vowell signed the back of the Kindle with a paint pen. Since I mentioned that 4 of her books were on it, she added, “4 books … so far”. Very witty lecturer and charming person, even if she did look a little tired and bedraggled at the end of the book signing.