In Post Crisis continuity, the only part from Crisis on Infinite Earths that supposedly happened was the last issue, when the Anti-Monitor made his last attempt to destroy the new and single universe, and all heroes traveled to the antimatter universe to fight him, but without Superman from E2, Superboy Prime and apparently, Wonder Woman.
During the second to last story from Mark Waid's The Flash run with Wally, Chain Lightning, Wally's memories shows that another part from COIE that was still canon was the antimatter cannon, and Barry sacrificed his life in order to destroy it. It's interesting because in that story, Wally has to save Barry sometime before COIE starts, so he can sacrifice later to save the universe during COIE. Wally fails in his mission and the universe was altered and completely destroyed, leaving only the antimatter universe ruled by Anti-Monitor. At the end Wally fixed his failure.
And Flash: Rebirth definitely has a lot of references to Waid's run, Morrison-Millar's mini-run, and Johns'run -over 150 issues- from Wally's series.
The Flash series between Rebirth and Flashpoint doesn't really involve Brightest Day story, you only need to know Captain Boomerang and Thawne came back to life at the end of Blackest Night, and they "earn" his life in Brightest Day. That's all, unless curiosity gets the better of you