Does Flash cost more?

This depends on what we will be doing with flash. If you are referring to a full flash website vs a full HTML website, then yes flash costs more, only because it will take more time to build the same website using flash.  I do not charge a higher hourly rate for flash vs ASP.NET vs HTML.  My hourly rate is the same across the board, its just that some technologies take longer to program than others.  When building a website the focus has to be on browser compatiblity and SEO, rather than just how it looks.  For this reason Flash is no longer a very popular choice among developers.