Can I ask a DST INSPIRE faculty for a recommendation letter?
In general, any mentor with good scientific or academic qualifications can be a good recommender.  It's always better to have somebody who can speak strongly about you, even if they're in a "non-standard" academic position.

That said, it's important that your letter-writer make it clear who they are and why their opinion should be taken seriously, especially when writing to an international recipient who may not know their system.  That might include explaining what a "DST INSPIRE" faculty position is, or it might just mean pointing at the letter-writer's own CV of scientific accomplishments.