You could use a moisturizing, dog friendly shampoo on her.
She could be flaky because of dry skin but maybe they have been using human shampoo...
I don't see bathing as a big deal and wouldn't hesitate to do it if I was dog sitting. She'll get over it as long as she isn't overly skiddish.
The shedding is one reason why I have a Yorkie.
Lint rollers and brushing is about all you can do and a good diet may help.