Pingali Venkayya is the correct answer. He was a Telugu freedom fighter who spent years studying flags from around the world before proposing a design for India's own flag. His original concept, shown to Gandhi in the early 1920s, went through changes over the next two and a half decades, and the final tricolour with the Ashoka Chakra at its centre was officially adopted just before India's independence in 1947.
None of the other names fit the role of designer. Gandhi supported and reviewed the flag concept but did not create it himself. Nehru's part was political, presenting the flag for adoption in the Constituent Assembly, not sketching its design. Tagore's legacy lies elsewhere, in literature and music, including India's national anthem, and he had no hand in designing the flag. So the credit for the flag's design belongs to Pingali Venkayya.