This is confusing
The 'flying king' rule is part of the international ruleset for draughts, but does not exist in the English Draughts ruleset, which is also known and played as American Checkers. So it depends which country you are in, and which rules variant you use.
King's corners, Checkers, King of the hill, and King Kong
In checkers, yes
yes
No
You can
Either a king or an ordinary playing piece may jump a king in a game of checkers in the United States of America. But the rules are different in Italy. Specifically, in an Italian game of checkers, only a king is allowed to jump a king.
no you can't
Yes
No.
yes
You'll just have to use some other kind of marker.