Not quite. People didn't add the H to make Antony mean "flower" - they assumed that the H should have been there all the time. So, they helpfully put it back to correct a mistake.
Except that it wasn't a mistake ... Antony is such an ancient name, and Etruscan is such a mysterious language, that we simply don't know what it actually did mean. Now, its meaning is: Nice name that my parents chose for me with love.
You might be interested to look at the comments for Anthony - click on it here, and then click on Comments.