I get the impression that time in Flash is a little "timey-wimey" and that as long as events happen reasonably close to when they were supposed to, that the timeline will stay intact. I'm not sure that Eobard is a descendant of Eddie or just a relation.
There's still the question of why Eobard is travelling back from the 25th century in the first place. Barry won't live that long and the timeline Eobard lives in will be well established. My suspicion is that Barry somehow goes to the 25th Century and messes up Eobard's life, so Eobard comes back to take care of Barry. I'm sure they'll cover Eobard's movites in the future (/rimshot).
However, Barry needs to be around in 2024 to complete his job in the "Crisis" so the future timeline will remain intact. After that, Eobard should be free to kill Barry? But Barry disappears in a flash of light. Ohhh... I wonder if Barry runs so fast in the Crisis that he goes forward in time! He messes with Eobard then they both go back to Barry's origin where episode 1 happens.
I still want to know what happens to the Barry that fought Eobard in the Allen family home.