All Tennis Players How Many Grand Slams Has Wilmer Allison Won? Wilmer Lawson Allison Jr. (December 8, 1904 – April 20, 1977) was an American amateur tennis champion of the 1930s.Wilmer Allison Has Won 1 Grand Slam. FacebookTwitterEmail How Many Grand Slams Has Madison Keys Won? How Many Grand Slams Has Jannik Sinner Won? How Many Majors Has John Isner Won?