This is a question I hear often from people who have read or have heard about the 5th Canto of the Srimad-Bhagavatam . The Bhaktivedanta Institute for Higher Studies will soon be publishing a book that deals with this issue in scholarly detail, but I can give you my personal view having gone through the different evidence. The short answer is: No, the Bhagavatam does not explicitly say that the earth is flat, though it is sometimes interpreted in that way.
In his purport to Caitanya Caritamrta (Madhya 24.256), he writes, “This is the process of initiation. The disciple must vow that he will no longer commit sinful activity — namely illicit sex, meat-eating, gambling, and intoxication. He promises to execute the order of the spiritual master. Then the spiritual master takes care of him and elevates him to spiritual emancipation.