Option 1: Bankim Chandra Chattopadhyay was an influential writer and poet in Bengal during the Indian independence movement. However, he did not design the national flag of Independent India.

Option 2: Rabindranath Tagore was a renowned poet, philosopher, and artist, and he composed the national anthem of India. However, he did not design the national flag.

Option 3: Mahatma Gandhi was a prominent leader in the Indian independence movement and played a crucial role in achieving freedom. However, he did not design the national flag.

Option 4: Pingali Venkaiah, an Indian freedom fighter and writer from Andhra Pradesh, designed the national flag of Independent India. His design featured the tricolor with the spinning wheel (charkha) at the center. This flag was adopted as the national flag on August 15, 1947, when India gained independence.

So, the correct answer is option 4.