Can we use the modal verb "could" to give permission?
Mr A: Could I take your car?
Mr B: Yes you could.
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Yes, you can. However, it's not entirely natural, and it normally requires more context than given in the question.
Mr. A: "I know you don't normally allow people to drive your car, but if I grab you that food you need, could I take your car?"
Mr. B: "Yes, you could."
In that context, it's made clear from the preceding context that could is associated with permission. Also note that the sentence was converted into a conditional (which makes could more natural).
These are all things that could be given in previous sentences too:
Mr. A: "You don't normally let people take your car do you?"
Mr. B. "No."
Mr. A. "But I know you need some groceries and, because you hurt your leg, you can't drive yourself. So, if I picked those up for you …"
Mr. B. "Yes?"
Mr. A. "Could I take your car?"
Mr. B. "Yes, you could."
More often, the person asking the question would simply say (without any of that additional context), "Can I take your car?" and the person answering would say, "Yes, you can" or "Yes, you may."
Even if the question is asked with could, the answer more commonly comes backs with can or may.
However, especially in formal English, some people will mirror back the word used.
For instance, even though it isn't typical, it's perfectly possible to hear an exchange like this:
"Might I have some of that mustard?"
"Why, yes, you might."
It's a form of exaggerated speech that's most often used as a kind of old-fashioned, upper-class affectation.