I read that we really could use the double possession like
It's a car of my father's
But somewhy we can't say:
It's a car of my father's friend's
Like, the triple possession? Is it true or we actually can avail of it, too?
You can use as many possessives in a row as you want.
For instance, this is perfectly grammatical:
It's a car of my father's friend's daughter's boyfriend's employer's wife's.
But while it's grammatical, it can become difficult to follow at a certain point.
In the case of your original sentence, it's short enough to be easily understandable—and there's no reason why you can't say it.
But you may be thinking of this construction instead:
It's a car that belongs to my father's friend.
In this case, the final noun doesn't use an apostrophe. The same would be true at only a single level of possession:
It's a car that belongs to my father.