After you follow the instruction here to create a Gift Card inventory for Development, you can then allocate a bunch of gift cards (for example, 20) to program so that they can distribute to their clients.
1: Navigate to the Development Gift Card inventory page.
If you're not sure how to locate this page, you can go to the "Items" Tab. A gift card inventory is a Item record.
2: Fill out Gift Card Allocation Screen Flow.
Program: Type to look up the program which you want to allocate the gift cards to.
Managed By: Type the PD's name to look up the User record.
Initial Quantity: amount, in number, of gift cards you're allocating to this program.
And then click "Next". Salesforce will automatically create a gift card inventory record for the program and will notify the "Managed By" person.