Question

Who is the goddess depicted as “Bharat Mata” & why is she having Indian tricolor flag?

Answer

Goddess

The Bharat mata is [primarily] goddess Durga. However in general she is an amalgamation of various goddesses.

Bharat Matā (Hindi, from Sanskrit Bhāratāmbā भारताम्बा; अम्बा ambā means 'mother') is the national personification of India as a mother goddess. She is an amalgam of all the goddesses of Indian culture and more significantly of goddess Durga. She is usually depicted as a woman clad in a saffron sari holding the Indian national flag, and sometimes accompanied by a lion... The Tiranga flag was also started being included during this period. In 1930s, the image entered in religious practice. The Bharat Mata temple was built in Benaras in 1936 by Shiv Prashad Gupt and was inaugurated by Mahatma Gandhi. ... The motto Bharat Mata ki Jai ("Victory for Mother India") is used by the Indian Army. [Wikipedia]

This is a rare combination of religion and nationalism (a part of Dharma).

Etymology

It was actually a painting work, which was named as "Bharat Mata". Eventually it got transformed into a worshippable figure for indpendence movement of India. The very early history of Bharat mata dates back to 1905 from a painting of Abanindranath Tagore:

Bharat Mata depicts a saffron clad woman, holding a book, sheaves of paddy, a piece of white cloth and a garland in her four hands. The painting holds historical significance as it is one of the earliest visualizations of Bharat Mata, or "Mother India." ... The "work" was painted during the time of the swadeshi movmement. The movement began as a response to the Partition of Bengal (1905) [source]

She is not a traditional Pauranic goddess.

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So in the oldest of paintings, there was neither tricolor flag with her, nor was there any lion. The flag started to appear around 1930's when the independence movement was at its peak as described in the above Wiki article.

Trivia

Here is what Sister Nivedita, a famous student of Vivekananda has to say:

From beginning to end, the picture is an appeal, in the Indian language, to the Indian heart. It is the first great masterpiece in a new style. I would reprint- it, if I could, by tens of thousands, and scatter it broadcast over the land, till there was not a peasant's cottage, or a craftman's hut, between Kedar Nath and Cape Comorin, that had not this presentment of Bharat-Mata somewhere on its walls. Over and over again, as one looks into its qualities, one is struck by the purity and delicacy of the personality portrayed. [Complete works of Sister Nivedita]

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