We have gone to Napa Rose twice and I have worn a nice but not too dressy summer dresses, both above the knee and spaghetti straps. (this was at the chef's counter and I did not feel underdressed)
Nothing like Victoria and Alberts, basically the same dress code as the parks.
You will see suits and evening dresses at one table, shorts with t-shirts at the next table.
As the others have noted, no the dress code at Napa Rose is not like V&A. Most people who go there do try to dress up a bit, but you'll still see some who have come directly from the park.
Ditto to above...folks tend to get a bit dressier for dinner but park casual is perfectly acceptable...but personally I would feel a bit outta place in a tank top, cut offs and flip flops.