Yes, warlocks can have burning hands in d&d 5e through specific subclasses, specifically the fiend and genie warlock. Typically, they cannot get their hands on it since it is not part of their spell list. However, thanks to the mentioned subclasses, it becomes added to their spell list. Read more about these subclasses in the “subclasses that can cast burning hands in d&d 5e” section above.