I've just finished Paste Email Plus v4.0beta. It now allows you to copy pastetext items to the clipboard so they can be pasted into flash forms (or anywhere else, for that matter).
As a test, I defined a category named "Some flash sites":

Then I created a couple of pastetext items in that category:

To copy the pastetext, right-click on a pastetext label (in the PasteEmailPlus drop-down menu) and click "Copy pastetext to clipboard":

Next you can paste the item into a flash input field by either using
right-click > Paste or
ctrl-vI've included the new version as an attachment below. This is a beta version, so to be safe, make sure to copy the file /pasteemailplus.json somewhere for safekeeping. If you find any bugs, you can always install your current PEP version and copy the data file back.