Looks like they negotiate with vendors to buy discounted gift cards, or store gift certificates.  
They then share a portion of the discount with the users on the app and a portion goes back to the Fluz company.

So they are using the buying power of the users as their leverage to get the in store discounts.  
Very interesting.

Vendor gets a sale, albeit at a slightly lower price, but they rotate stock.
User gets a product at a lower price
Fluz company gets a little bit of cash back from the sale

More users join network
More sales gives little bits of additional cash back to other users

Edit:
From their telegram, they've evidently signed a contract with a major grocery store chain in New York.