@JonathanReez Are you interested in whether it is legal to do so? I suspect that the terms of service forbid it without a license, but that's just speculation really.
@JonathanReez Copyright is not the only law in play here.
@JonathanReez Linking back to timatic would only help if it satisfies their terms of service.
@JonathanReez Also, the non-copyrightability of a fact does not imply that a compilation of facts cannot be protected by copyright. See 17 USC 103 for example.
You also have to consider that you will probably have to worry about copyright law in other jurisdictions as well, unless you and all your users are only in the US.
@JonathanReez the applicability of the phone book case to this one would be an open question. It's not clearly the same.
The idea that not charging money would absolve you from copyright infringement liability is bizarre. If that were true, there would be no penalty for freely distributing pirated copies of movies, books, music, etc. It's not only about whether the infringer makes money; it is more importantly about whether the infringement deprives the copyright owner of revenue.