To answer this question, we need to have knowledge about the characters and their flags in the Mahabharata.
Option A) Karna - This option is incorrect because Karna's flag did not carry a cobra on it. Karna's flag was known as Vijaya, which depicted a chariot wheel.
Option B) Arjuna - This option is incorrect because Arjuna's flag did not carry a cobra on it. Arjuna's flag was known as Hanuman, which depicted the monkey god Hanuman.
Option C) Bhima - This option is incorrect because Bhima's flag did not carry a cobra on it. Bhima's flag was known as Vayu, which depicted the wind god Vayu.
Option D) Duryodhana - This option is correct because Duryodhana's flag carried a cobra on it. Duryodhana's flag was known as Kataka, which depicted a cobra.
Therefore, the correct answer is option D) Duryodhana. This option is correct because Duryodhana's flag carried a cobra on it.