Showing Discount labels for products that are linked to any discount offer?
If by "ID field" you mean the name of the discount shown to customers, this is doable.

You must have a product that is the object of a "Free product" offer.

Once that is done, you'll need to add two relationships to the view. The first, you've already gotten is the link from the product to the offer: 


  Commerce Discount Offer referencing products from commerce_free_products
  Trade Discount Offer referencing products from commerce_free_products


The other relationship is the link from the offer to the Discount entity itself:


  Commerce Discount referencing Commerce Discount Offer from commerce_discount_offer
  A bridge to the Commerce Discount entity that is referencing Commerce Discount Offer via commerce_discount_offer


Then you can add fields attached to the Commerce Discount entity:


Commerce Discount: Name
Commerce Discount: Admin title


And now your labels should be visible.