Found this great list of Barry Allan’s best stories for long time fans, or new fans (maybe even of the show!) looking for a little more info on the speedster.
_________The Mystery of the Human Thunderbolt
_____Showcase #4 / Secret Origins Annual #2
Credited with kickstarting the Silver Age of Comics and def one of the landmark issues for Flash and ALL comics really.
__________The Brave and the Bold
_____Flash & Green Lantern: The Brave and the Bold #1-6
The origin of the bromance that is Barry Alaln and Hal Jordan, aka Flash and Green Lantern. It’s so awesome to see how Flash and GL interact and their friendship as it grows.
__________The Flash of Two Worlds
_____The Flash vol.1 #123
One of the greatest comics ever written, Flash or otherwise. This is the story that brought us the Multiverse and saw Barry meeting the original Golden Age Flash, Jay Garrick.
__________Flash vs. the Rogues
Barry’s first encounter with The Rogues, one of the best villains groups in comics. It’s got the original lineup of Rogues including Mirror Master, Heatwave, and Captain Cold.
__________The Death of Iris Allen
_____The Flash vol.1 #275-284
Unfortunately DC isn’t printing this part revenger, part time jumping adventure so you’ll have to do some looking, but the story of Barry’s fight against Professor Zoom after Iris’ death is really awesome.
__________The Final Fate of the Flash
_____Crisis on Infinite Earths #8
With comic book heroes death is rarely permanent, but when Barry sacrifices himself to stop the Anti-Monitor he was gone for over 20 years real world time. It’s a great story, and definitely a must for any Flash fans.
__________The Life Story of the Flash
Massive collaboration is the one stop shop for anyone who wants to catch up on the life and times of the Flash. It’s actually really neat because it’s told from Iris’ perspective and goes through Barry’s entire career and has original content too.
_____The Flash: Rebirth #1-6
The resurrection of the Flash after he died in 1985 in Crisis. This is seriously the best revamp in comic history, taking an awesome, but kinda dull and out dated hero and making him relevant to modern readers and fans.
The story is a little messy but Barry’s personal struggle is one of the most emotional things you’ll read. Flashpoint was the turning point for the DC relaunch in 2011 but it focuses heavily on Barry and his own story.
_____The Flash vol.4 #20-23, #23.2, #24
The last and most recent Flash editions and the one that rebooted Reverse Flash as ruthless and terrifying. Reverse is considered the beginning of the new “grim and gritty” look of the DC universe.