If you are related to him, it’s probably not through Marvin Jr. Marvin Jr.’s children were born in the 1950s, which means they’re probably around the same age as your grandma. If your grandma was one of them, that would make Clyde Barrow her great-uncle… something that she would surely know. The relationship (if there is one) probably comes through a different branch.
Being related to someone means that you share a common ancestor. If you don’t know who your own ancestors are, it’s impossible to know if you have an ancestor in common with someone else. Take Maxi and Shirley’s advice and work on your own family tree first. Then you can compare it to Clyde’s family tree and see if it merges somewhere. I would also ask your grandma for some more details. How does she know about this relationship? Who told her? If someone else has already researched your family tree, they might have the answer.
Also keep in mind that sometimes people use the word “related” loosely. My mom always said we were related to Kenny Rogers, the country-western singer. As it turns out, it’s her cousin’s husband who’s related to him. Although we are related to this cousin, we aren’t related to her husband, and thus not to Kenny Rogers, either.