There have been discussions here before, but Shaunsyd is right.
The Cooper S plastic-chrome dress mould is enough to hold them against the body.
The parts you bought always came in the factory accessories kit but were not really used by anyone, including the factory.
You were meant to drill holes in the guards and push in the flat buttons that became hooks to mate up with the slots in the inside edges of the flares.
The metal trim clips were meant to hold the outer edge of the flare to the steel strip then be covered by the plastic mould.
Attachment:
Rivet rear flare.jpeg
The flares were riveted to their backing strip at the very front and rear with fibre washers.
People usually pop rivet the plastic chrome at either end of the wheel arches too. But you rivet from the underneath with short rivets or they will poke into the top of the mould.
Also suggest just fitting the mounds and leave for a while before final cutting, riveting, etc as the mould will shrink and move.