Katie Dix, from the Story of Vintage Hankies, had the following to say about collecting Fourth of July hankies.
Be on the lookout for Fourth of July hankies while you are antiquing and flea market shopping. Handkerchiefs actually printed with “Fourth of July” or “Independence Day” are extremely rare and therefore very collectible. Hankies with a patriotic theme are fun to find and more available. Watch for Know Your Presidents, Democratic Party, Republican Party, The Star-Spangled Banner, Early American Historical Events and others from the 1950s - the Golden Age of Hankies. Expect to pay $25 to $30 for handkerchiefs with patriotic themes in very good condition.