How is the exchange rate determined for giving Zakat on foreign currencies in local currency? Is it based on the current exchange rate, the average exchange rate throughout the year, the black market rate, or the bank rate?

The basic principle is that zakat (definition) should be paid from the asset itself. Paying zakat from the foreign currency itself is more cautious. However, if the zakat payer wishes to pay zakat in another currency, there is no harm, provided that the actual value of the currency at the time of payment is taken into consideration.