I just did a few quick tests and can confirm that the flags and their state
(checked/unchecked for the Flags which support this) *are* carried over when
both copying and cutting.
The trick is to ensure that you are also selecting the last "blank"
character in the line or paragraph being cut/copied. Think of it like the
Paragraph mark in Word.
If you select with the mouse up to the last character, or do a home,
shift-end before copying/cutting, then the flag will not be placed on the
clipboard. If you Select All (or press Ctrl-A) the flag will be placed on
the clipboard. If the item in question is in its own container, you can
select the container handle bar at the top.
Hope this clears it up for you.