It depends on how much you want them to scale it up. If it is a 10% scale, and you scanned your images at greater than 200 dpi, it shouldn't be an issue. If you scanned them at 72 dpi, and you need them to quadruple the size, it's going to look like total garbage. They don't have any magic non-destortion tools. Give us the specs of your files, and I can probably give you more details.
Also, good luck with Kinko's getting it right... I have zero faith in them. The only thing good I can say about Kinko's is that they have deep pockets and might give you something free if they screw up. But that's just one man's opinion.