Depends, there isn't really a flat rate that most designers charge.
It depends on skill, experience, education, type of work, and designer preference.
I personally charge $150/hr and the service price (ex. Website $500.00 + $150/hr), but everyone kind of does it differently.
I'm building a site site with a specific audience in my area, in my spare time and learning everything as I go. I'm hoping requests for web design might come from my site users. What would be a reasonable fee for ME(no experience & constantly learning etc) to charge?
I figure a flat competitive fee plus external costs would be appropriate. It's probably a bit cheeky asking for an hourly rate when a grad can achieve 10 times what I can in an hour