Where do currency exchange businesses get the currency they sell?

The answer is the designated bank or the central bank.

Lets take the US Dollar for example. In particular country, a US Dollar clearing is done by some commercially designated bank. Let’s say in Philippines, this would be Bank D’Oro (BDO). So BDO would be designated as the US Dollar correspondent bank in Philippines. A commercial bank in the US (say Citi) would arrange for cash US Dollars to be flown into Philippines and handed over to BDO. Yes, currency is actually hauled in specialized flights and handed over. BDO now has US Dollars.

The same in many cases is done by the Central Bank of a country. Since most central banks might be keeping part of the US Dollar reserves, they too would contact their counter-party US Commercial Bank and ask them the same.

In reality, certain regions are handed over to certain banks. For example, distribution of US Dollar notes for Gulf Countries might be with HSBC and Standard Chartered Bank. These two banks would have a commercial arrangement to ship physical currency notes to these countries.

Once the notes are in the countries, currency dealers can then go to the designated banks and exchange their foreign exchange credit with currency notes.

Whenever a currency dealer has more cash, they take it to the designated banks and exchange it for a digital credit and vice versa.