The flare is caused by the way the pleats are sewn down - they are like darts in a way, and they function as such.

Take a look at how the pleats have been made - is the grain running straight along the edge of the outer fold of the pleat from the waist to the hem?

If so you can just cut the stitches which hold the edge of the pleat to the fabric below, possibly you will only need to take out the lower half, so that the flare is no longer insisted upon.

You might need to assist the change in shape by pressing in a new fold on the inside.

What might be more relevant is the alteration in the aprons from left to right closing. Is the under apron 'presentable'? The over apron is usually carefully placed on the pattern so as to look centered, it also has a shaped edge and sometimes a fringe. The under apron normally has a straight edge. Before undertaking any work it might be as well to check that the swapping of the aprons is possible.

If the apron has darts you might need to take them out so it lies flat when it becomes the under apron.

I have done some costume making - it seems that fate always conspires to supply the least useful items for our purposes.

Anne the Pleater