A modern website needs to be accessible on PCs, tablets, and smartphones. While there are arguable reasons for segmenting off the last option as an outlier (though some devices offer the resolution and capabilities exceeding some desktops), it is less justifiable making a distinct version for a tablet.
So you end up making a rich "HTML 5" version for tablet and smartphones.
Why, then, would you bother with Flash for the PC? If you have a modern simile for Tablets, Flash is just completely redundant.
Flash is a sign of a derelict site. It would be hard to justify its use for greenfield development.