I see a lot of reading order questions and where to begin questions. I have tried to compile an exhaustive list of all the Post Crisis Batman comics in the app in “chronological” order (not necessarily order in which they were published). My main criteria in this timeline is to preserve the order of events as you read. For example, we see the Batsignal used in Gothic, which was published before Prey, yet in Prey, the Batsignal is still a prototype – hence the adjusted placement in the list below. Other considerations are Jim Gordon’s status in the police department and who plays Robin.
I have omitted stories where the full run isn’t available in the app - see The Dark Knight Returns 
An asterisk denotes recommended titles.
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POST CRISIS - Batman issues here are in the app under Batman (1940-). If you want to start with New52 or Rebirth, skip down to those sections.
Batman: Legends of the Dark Knight was a series chronicling Bruce's early days as Batman, so we begin here.
*Batman Shaman
- Batman: Legends of the Dark Knight #1-5
*Batman Prey
- Batman: Legends of the Dark Knight #11-15
*Batman Gothic
- Batman: Legends of the Dark Knight #6-10
*Batman Venom
- Batman: Legends of the Dark Knight #16-20
Batman Faith
- Batman: Legends of the Dark Knight #21-23
Batman Flyer
- Batman: Legends of the Dark Knight #24-26
Batman Family
- Batman: Legends of the Dark Knight #31
Batman Blades (TPB Batman: Collected Legends of the Dark Knight)
- Batman: Legends of the Dark Knight #32-34
Batman Sanctum (TPB Batman: Dark Legends)
- Batman: Legends of the Dark Knight #54
Batman Quarry
- Batman: Legends of the Dark Knight #59-61
*Robin Year One
- Robin Year One #1-4
Batman Strange Apparitions (TPB, partially collected)
- Detective Comics #471-476
*Batman Faces
- Batman: Legends of the Dark Knight #28-30
Batman Second Chances
- Batman #402-403, 408-416
Batman Year Three
- Batman #436-439
A Lonely Place of Dying
- Batman #440
- New Titans #60
- Batman #441
- New Titans #61
- Batman #442
Batman Shadow of the Bat (TPB "" Vol 1)
- Batman Shadow of the Bat #1-12
Batman Vengeance of Bane
- Batman Vengeance of Bane #1-2
Batman Harley Quinn
*Batman Under the Hood
- Batman #635-641, 645-650
- Batman Annual #25
Batman Detective (TPB, partially collected)
- Detective Comics #821
- Detective Comics #826
The following titles are part of Grant Morrison's massive run. I would be remiss if I didn't urge you to read the run in its entirety, as it is very involved. At the very least, read summaries of the missing pieces to keep up on the references. This is a pretty good list of the run with short summaries - https://thegothamarchives.com/grant-morrisons-batman-reading-order/
*Batman and Son
- Batman #655-658
*Batman RIP
- Batman #676-683
*Batman & Robin Vol 1
- Batman & Robin #1-6
*Batman & Robin Vol 2
- Batman & Robin #7-12
*Batman & Robin Vol 3
- Batman & Robin #13-18
*Batman The Black Mirror
- Detective Comics #871-881
End of Morrison saga, save for the Batman Incorporated titles.
Batman & Robin Vol 4
- Batman & Robin #19-26
Batman Incorporated (2010-)
- Batman Incorporated #1-8
Batman Gates of Gotham
- Batman Gates of Gotham #1-5
Read Flashpoint here if you want to know what sparked the New52.
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NEW52 - Batman issues here are in the app under Batman (2011-). Batman's early days are retold in issues 21-33, hence their placement at the top. There's no problem in reading them in publishing order (that's how we read them when they came out), but I like to reset his origin story here with the reboot.
Batman Zero Year - Secret City
- Batman #21-24
Batman Zero Year - Dark City
- Batman #25-27, 29-33
Batman and Robin Born to Kill
- Batman and Robin #1-8
*Batman The Court of Owls
- Batman #1-7
*Batman The City of Owls
- Batman #8-12
- Batman Annual #1
Batman and Robin The Pearl
- Batman and Robin #0, 9-14
*Batman Death of the Family
- Batman #13-17
Batman Incorporated (2012-) (TPB Batman Incorporated Vol 1 & 2 Demon Star and Gotham's Most Wanted)
- Batman Incorporated #1-13
Batman Graveyard Shift
- Batman #18-20, 28
- Batman Annual #2
Batman Eternal
- Batman Eternal #1-52
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Rebirth
I will defer to Nathan.Payson's already wonderful Rebirth Reading Order thread (include the last dash in the URL)
https://www.dcuniverse.com/community/boards/comics/dc-universe-reading-order-
Elseworldy Stories - Not in continuity, can be read any time you like.
Batman Europa
- Batman Europa #1-4
Batman Year 100
- Batman Year 100 #1-4
That about wraps it up. Let me know if I'm missing anything or something looks out of place.
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