How can I repair the peeling paint on the metal flashing of my vinyl?
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If you are talking about the metal transition strip, you might just be better pulling up the strip and replacing it with a new one. Most hardware stores sell them pretty cheap.
Take a good photo to the paint dept. of your home improvement store and ask for their advice.
Better yet always go to a stand alone paint store for real paint questions. The associates there are usually trained were as the workers at the large home improvement stores are usually temp help.