Kindly grant me leave from 14/4/2017 to 20/04/2017 for this I highly obliged to you Thanks &Regards Is this the correct sentence to take leave from bos
It depends on where you live and work. "Kindly" is not as frequently used in American work settings as it is in India.
Also, you should add "am" in "I am." As in, "I am highly obliged to you."
Personally, I would write,
Could you please grant me leave from 14/4/2017 to 20/04/2017? I would greatly appreciate it. Thank you, ...
But I am speaking as someone who works in Chicago, Illinois in the U.S.
Again, it depends on your workplace and culture. Do whatever is customary in your workplace, if writing it exactly as written is something your boss would understand and appreciate, then it's the correct thing to write.
Having lived in a country for several years where many of the people I know are from Southern Asia, I think the most common way of writing this would be:
"May you/Could you kindly grant me leave from 14/4/2017 to 20/04/2017? For this I would be highly obliged to you. Thank you and Regards."
I think this is a slightly more formal version of what you said, and I have seen similar methods of writing formally from people I know.