Is it permissible to use a credit card from an Islamic bank to collect airline miles by allowing a relative to pay bills and acquire goods with it, then recovering the amount in cash from him?

If the Shariah controls mentioned in the previous fatwa (definition) are met, then there is no objection to benefiting from the credit card and the points granted when using it.

As for giving the card to your friend for him to benefit from it, it appears that this is not permissible as long as the purpose is to gain points, because this is considered a loan that draws a significant and intended benefit, which is gaining points. This is a loan that yields a benefit, as a loan is only permissible if the lender intends to benefit the borrower purely for the sake of Allah the Almighty.