Um no, the credit card companies may not allow this rather than Amazon! Their usual rule is that goods may only be ordered online for delivery to the actual credit card billing address -- it's a sensible rule to prevent misuse of your credit card if stolen.
You may be able to get away with buying something as a gift -- I've not tried that. Alternatively if you want to go through the hassle you may be able to convince your CC company to waive the 'original billing address only' rule, but certainly the times I've tried it it's been a pain!
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