That what speed wraiths are there for. They would be chasing evil Barry non stop, he's no Thawne.I think the idea would be that evil Future Barry is making TONS of changes to the timeline on a catastrophic scale, so Thawne has to stop him because it risks destroying the entire multiverse.
Like, imagine if they did the Future Barry story arc where Barry travels back from the future to prevent Iris' death, only instead of stopping there he goes "Wait, I can fix ANYTHING I WANT now" and starts shredding the timeline by mucking about with events across time. If Flashpoint was a surgical scalpel to the timeline changing one event that created huge ripple effects, this would be more like someone drunkenly taking a meat cleaver to it.