What is the latest that someone can have a growth spurt?

It Depends. This is a complicated question because the pubertal growth spurt of any child is inherently dependent upon the age at which the child reaches a particular point in puberty. If the child has a pubertal delay, the pubertal growth spurt may not happen until later teen years. On the other hand, it may take place much sooner if puberty started at an earlier age.
Sometimes 19 yr male. In order to have a late growth spurt in height, a young man's growth plates in his leg bones must still be open (not fused closed). Usually, any late growth spurts are at age 17-19, and tend to be genetically determined, so other male relatives may show a similar growth pattern. Growth spurts after age 19 are very unusual, but with over 3 billion males on earth, such spurts possibly could happen.
Growth plates open. Is depends on the sex and the family history usually by 16-17 every child may have had a growth spur. Usually you have to have your growth plates open for that to occur.
Grouth plates open. Growing bones have plates of new growth located just before the bone ends. These growth plates have less density than bone & show up on xray as a dark line like a crack. As long is there are actine growth plates, there is potential for more growth in that bone. A hand xray is often studied in short kids to see if they have more time to grow. If the growth plates have closed linear growth is done.