Perhaps start with a tighter fitting cork. They are available in a variety of diameters.
Boiling a cork may restore its diameter a little.
Some technicians put paraffin wax over the cork, position the cork in the head, then heat the head to melt the wax, presumably to seal the cork in the tube.
I don't think many technicians would attempt to re-use a loose cork. A well-sealing cork (and that means at the embouchure hole end of the cork) is very important for a flute.
Boiling a cork may restore its diameter a little.
Some technicians put paraffin wax over the cork, position the cork in the head, then heat the head to melt the wax, presumably to seal the cork in the tube.
I don't think many technicians would attempt to re-use a loose cork. A well-sealing cork (and that means at the embouchure hole end of the cork) is very important for a flute.