If not the recent stuff, you can always go a bit back and see some of the old stuff. CRISIS ON INFINITE EARTHS has the death of Barry Allen, who he seems to be a big fan of, and it's a classic story. You might also want to look into Mark Waid's Flash stories. They're a bit more expensive, but they're out there, and they're classics. I found some on Amazon:

http://www.amazon.com/The-Flash-Born-Mark-Waid/dp/1563895048

http://www.amazon.com/Flash-The-Return-Barry-Allen/dp/1563892685/ref=pd_sim_b_1?ie=UTF8&refRID=0QRBHZHVR4FJBFYXD9CJ

http://www.amazon.com/Flash-Terminal-Velocity-DC-Comics/dp/1563892499/ref=pd_sim_b_1?ie=UTF8&refRID=0ZC3PGMKXT7TDQX1HJTX

http://www.amazon.com/Flash-The-Dead-Heat-Comics/dp/1563896230/ref=pd_sim_b_3?ie=UTF8&refRID=0ZC3PGMKXT7TDQX1HJTX

Since you've already read New 52 there isn't really a defined order to follow... but there is some recommended reading on the sidebar. Of all those definitely, definitely read Flashpoint, not just the Flash main story but Project Superman and Knight of Vengeance are great one-offs for those characters too. I also really like Born to Run And if you read Flashpoint and liked Flash interacting with other big namers read Crisis on Infinite Earths it's one of the biggest DC events and features some epic Flash action

Aww, then in that case I highly suggest you pick up Born to Run, that's a good one to start you off with. Maybe The Return of Barry Allen (this one will be better to get on Comixology actually), too for a really good story with every speedster introduced succinctly.

And if you want some good Caitlyn, look for her Villain's Month issue. It's a pretty good New 52 introduction of the character and what she's all about.

Mark Waid's Flash hasn't been collected in omnibus format, and it's not too likely to be in the near future (he split up with DC a few years back after getting sick of Dan Didio, especially the editorial interference while writing the awesome 52 weekly series. Sad, as apparently Waid could have been the EIC of DC at one point).

You can find TPBs of Born to Run, but it's very expensive - digital is $4, the TPB is $30 (used).

Here's Geoff Johns' Flash Omnibus vol 1 - but with the Comixology sale going on, the digital version is less than half the price of the omnibus.

https://www.amazon.com/Flash-Born-Run-Mark-Waid/dp/1563895048/ref=sr_1_1?ie=UTF8&qid=1466645584&sr=8-1&keywords=the+flash+born+to+run
would this cover issues 62-65 like recommended? im new to comics and general and understand there are issue numbers but not how they work with different stories

Modern DC Character Origins

• Aquaman | Time and Tide - David | The Trench - Johns
  
• Batgirl | Year One - Dixon, Beatty
  
• Batman | Year One - Miller | Zero Year - Snyder
  
• Deathstroke | The Judas Contract - Wolfman | Deathstroke, The Terminator: Full Cycle
  
• Flash (Barry Allen) | Rebirth - Johns | The Flash - Manapul, Buccellato
  
• Flash (Wally West) | Born to Run - Waid
  
• Green Arrow | Year One - Diggle
  
• Green Lantern | Secret Origin - Johns | DC: New Frontier - Cooke
  
• Hellblazer | Saga of the Swamp Thing #37-44 - Moore | Hellblazer #1-13 - Delano
  
• Joker | The Killing Joke - Moore | The Man Who Laughs - Brubaker | The Joker - Azzarello
  
• Nightwing | Year One
  
• Red Hood | Under the Red Hood
  
• Robin (Dick Grayson) | Year One - Dixon, Beatty
  
• Shazam | The Power of Shazam! - Ordway | The Monster Society of Evil - Smith | Justice League back-ups #0, 7-11, 14-16, 18-21 - Johns
  
• Superman | The Man of Steel - Byrne | Birthright - Waid
  
• Swamp Thing | Saga of the Swamp Thing - Moore
  
• Teen Titans | The New Teen Titans v1 - Wolfman | Teen Titans v1 - Johns | Year One - Wolfram
  
• Wonder Woman | The Legend of Wonder Woman - De Liz | The True Amazon - Thompson | Wonder Woman - Azzarello | The Lies/Year One (Rebirth) - Rucka
  
  Suggestions to improve this list are welcome.
  
  EDIT: Added Shazam! suggestion
  

Volume 4 is considered the end of the good run on Flash, the newer volumes aren't nearly as good but they are enjoyable. My recommendation would be to start with Waid, and then begin with Manapul's New 52 Flash, by that point you should be able to judge whether you still have money left and you want to risk it with Volume 5.

As for Waid's run. You could try digital comics, I bought a bunch of arcs from his run on Comixology in a sale a while back. The easiest way to start would be with the Born to Run arc, which recounts Wally's origin as Kid Flash, and it's collected in tbp here http://www.amazon.com/The-Flash-Born-Mark-Waid/dp/1563895048
The arc I got after that was The Return of Barry Allen, which is a really good start of Wally's tenure as The Flash after the events of Crisis on Infinite Earths. Tbp here http://www.amazon.com/Flash-The-Return-Barry-Allen/dp/1563892685

After that, you could just buy as many trades as you want, for specific arcs, look at the sidebar here and in r/DCcomics, there were lots of recommendation posts from the sale I mentioned before. Hope this helps!

If you're interested in seeing the basis for a lot of what you've seen on the Flash TV series, you'll want to start with Flash, Vol. 2 #62 and basically read forward from there. This is the beginning of the Mark Waid era of the book, and you can find his first story arc collected in Born to Run.

This may seem a weird place to start because Wally West is already the Flash (not Barry Allen). But Waid does an amazing job of digesting all the older continuity (much of which, in reality, is buried in stories of questionable quality) and finding ways to incorporate them and reinvent them as he basically creates the entire foundation for the modern Flash mythology.

Actually reading Waid's full run can be difficult because it's never been fully reprinted. You can at least follow the highlights, though. (See Waid's bibliography for details.)

Basically, though, you can just read from #62 all the way through to the end of Volume 2. With the following inserts:

• Read Impulse #1-9 after Flash #101
  
• Read Impulse #10 after Flash #109
  
• Read Impulse #11 after Flash #110
  
• Read Impulse #12-13 after Flash #111 (after this point, IMO, Impulse becomes mediocre-to-terrible and isn't worth pursuing)
  
• Read Flash: Fastest Man Alive #1-13 and then All Flash #1 after Flash #230
  
  After you reach the end of Volume 2, read:
  
  
• The Flash: Rebirth #1-6
  
• The Flash: Volume 3 #1-12
  
• Flashpoint #1-5 (if you want to read the rest of the event tie-ins, they're mostly pretty good, but not necessary)
  
  Although there a few dips in quality during this long run of comics, they usually don't last for more than handful of issues. I recently did this full run (pun intended) and, IMO, it's well worth the time.
  
  I have not followed the book post-Flashpoint. But that's basically just Flash Volume #1-52, so it's pretty straightforward.