User blog comment:ReverseZoom101/Something about Episode 1 of The Flash: Season 5 doesn't sit right.../@comment-3221148-20181030181008

This "plothole" happened back in Season 1, when Eobard was able to check the newspaper when Blackout took away Flash's powers and the future changed accordingly. Guess Gideon just has some sort of timeline possibilities projector... which the Legends' Gideon actually had since Season 1 (when showing how the future would change depending on what happened to Vandal Savage, the Firestorm Matrix and other stuff).

So it's not a literal newspaper he brought together with him. It's a projection of future newspapers depicted by Gideon.