In Flash (2014), we're introduced to Eobard Thawne, the Reverse Flash, who was born in 2151. In Legends of Tomorrow, we're introduced to Rip Hunter, in the year 2166. Logically, Eobard would be aware of the events of 2166. Yet, from what little we hear Eobard say about his past in the 2100s, it seems decidedly different from the 2166 we see Rip come from.
In Rip's time, Vandal Savage has taken over the world, which is then in a brutal dystopia. Eobard mentions reading up on the events of the present day in history books, and being a distinguished member of his family. No mention of struggling to survive a brutal world or the global conflict that preceded Savage conquering the world.
Admittedly, both have their own Gideons, which suggests they're both from the same timeline. But it's not concrete that this means they're from the same timeline, given that Gideon probably originates in the more immediate future.
Do Rip Hunter and Eobard Thawne originate in the same timeline?