From what I know, since your product would essentially be free, it should be non-commercial. Further derivative ways of gaining money through the product could be through advertising since non-commercial as defined by CC means you can't take commercial advantage either if the product leads others to buy your other products, should you have any.

CC says it made the non-commercial licenses sort of murky on purpose so they can be more flexible. It's kind of annoying since the above is my interpretation due to their definition not being entirely clear. (I'm not a lawyer either.) Ultimately, if no one else provides an answer here I would seek out someone who is at least versed in the public domain and/or CC licenses.

Good luck!

Edit: I found this quote in the Tate site:

"If you wish to use the images in a commercial context (anything that has a monetary value, is promotional or related to a commercial company or charity) or need a larger digital file, please contact Tate Images..."

So yes a promotional context is disallowed from what I'm understanding. If you don't use it in any of those ways, I think you're fine but again I'm not a lawyer.