I am just wondering how to go about of getting an unknown cuttings from the parks, churches or roadsides. Who should I get permission from? Or is it ok just to clip those cuttings without asking permission? In case I find any fig trees during my travelling.

Someone's home, or a church just ask them.  A park, as long as there is not sing stating that is a historic tree, I would not worry about it.  The roadside, as long as it is on privet property, no one will likely care.

Rule of thumb - Always make some kind of an effort to ask someone, even if the tree is on an empty lot or somewhere that doesn't look private.

Ask when possible; ask forgiveness if not ;-)

That's been my position on many things for a long time.

Hi,
If the tree is big enough, taking 3 cuttings won't hurt. Of course, don't go advertise everywhere so that other 300 people won't go take 3 cuttings ...
In front of a church or near a fence as long as the branches are after the fence and in the public field/street ...
In the park, the park being public, 3 cuttings when no one is locking at you, send a smog bomb to the ground, in you vanish like a true ninja ...
Only limit, I wouldn't go neither advertise, nor sell those cuttings. I'll use them for me, and if needed be, propagate mine and sell from mine.
Just my way of thinking ... Don't get caught in the act ... By the way ... For that could be embarrassing . LOL .

I have had no refusals to-date when I asked

Thanks everyone for the advice.