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India has a diverse range of languages and accents. Moreover, people from different parts of the country have different accents of speaking the same language as well. For example, a person from Gujarat state tends to speak English in an altogether different accent than a person from Karnataka state.

The accents add the local flavor when heard/spoken and I want to create the same flavor in writing. Instead of simply writing: "....in typical Gujarati acccent...", I want to add something more that gives that flavor to a conversation, but I am stuck here.

How to do a fair description of accent? And Is it even possible to describe an accent instead of just mentioning so much so that even the person who is unaware of that accent get to know it?

I don't think you should describe the accent, what you should describe is the effect that accent has on a listener.

Obviously if the listener has the same accent, then the effect is zero. (An exception; if the listener is not expecting to hear their own accent. h/t to @Spagirl comment.)

But if listener has a different accent, what about the other accent causes reaction in them? Are they mentally translating, not recognizing words or being distracted by the pronunciation of the words?

For example, as an American professor listening to Indian students, I have to make an effort to concentrate and NOT be distracted by the far more musical tones of Indian speech when the students are just speaking English. I can lose track of what is actually being said, because of how it is being said.

Sometimes foreign students will truly mangle the pronunciation of English words to the point I get distracted trying to figure out what they are talking about. The same thing can happen with accented speech. It can sound funny (humorous) to a person, or confusing, or just so wrong it is unintelligible.

In America, different regions can have different words for the same thing; like "pop" vs "soda" vs "cola". When I travel, I find it mildly irritating to have to mentally translate regional dialect.

So instead of trying to duplicate in a reader the sound of what is happening, and hoping readers will realize the same effect, instead try to describe the effect of the accent directly. Both the overall effect, and perhaps specific effects on phrases or words.

Simply telling, e.g.

he said with a heavy Gujarati accent

would be my solution, but you say that isn't enough for you. Which is fair.

What is the most characteristic aspect of the accent you wish to describe? What would stand out most, and make it most recognisable? Is it the way a certain vowel is pronounced? Or some consonant? Is it that particular words are pronounced differently? I would focus your description on the element that stands out most.

For example, if I were describing the speech of a man from rural Andalusia, I might write

"The event will commence" - he pronounced it 'commenthe' - "at ..."

Or I might just describe:

His 'S's and 'Z's were all soft 'Th's, making it hard for me to follow what he said.

Of a woman from France, I might write

Her English was impeccable, except that her 'N's had a slight nasal quality.

In addition to accent, it might be that a person from one place would use particular words more often than a person from another place. Such distinctions are more related to dialect than to accent, but they too offer a way to convey the location flavour you're looking for.

What I would avoid is spelling out the accent phonetically (see also tvtropes Funetik Aksent). Unless done very sparingly, it is distracting, and it can be particularly hard to read for English-as-Second-Language speakers, who are, according to this source, ~70% of all English speakers. Do take a look at the tvtropes link however for some examples of phonetic accent done well (and some examples of it being done badly).