A strictly chronological reading order including all short stories, graphic novels, and the few canon novels, I think, works as such:
Broken Vessels
How Koshchei Became Deathless, Parts 1-2
Baba Yaga’s Feast
The Burial of Katharine Baker
The Calm Before the Storm
Witchfinder - Murderous Intent
Witchfinder - In the Service of Angels #1-5
Witchfinder - Lost and Gone Forever #1-5
Witchfinder - Beware the Ape
Witchfinder - The Mysteries of Unland #1-5
Witchfinder - City of the Dead #1-5
Witchfinder - The Gates of Heaven #1-5
Witchfinder - The Great Blizzard
Rise of the Black Flame #1-5
Lobster Johnson - The Burning Hand #1-5
Lobster Johnson - Caput Mortuum
Lobster Johnson - Satan Smells a Rat
Lobster Johnson - Tony Masso’s Finest Hour
Lobster Johnson - A Scent of Lotus #1-2
Lobster Johnson - The Prayer of Neferu
Lobster Johnson - Get the Lobster #1-5
Lobster Johnson - A Chain Forged in Life
Lobster Johnson - The Glass Mantis
Lobster Johnson - Garden of Bones
Lobster Johnson - Mangekyo
Lobster Johnson - The Forgotten Man
Lobster Johnson - Metal Monsters of Midtown #1-3
Lobster Johnson - The Pirate’s Ghost #1-3
Lobster Johnson - The Iron Prometheus #1-5
Lobster Johnson - Kung Pao Lobster (this may not be canon)
Lobster Johnson - The Killer in My Skull
BPRD - And What Shall I Find There?
BPRD - Bishop Olek’s Devil
Rasputin - The Voice of the Dragon #1-5
Sledgehammer 44 #1-2
Sledgehammer 44 - Lightning War #1-3
BPRD - 1946 #1-5
Hellboy - Pancakes
BPRD - 1947 #1-5
BPRD - 1948 #1-5
BPRD - Vampire #1-5
Hellboy - The Midnight Circus
Hellboy - The Other Side of Summer (prose short story)
Hellboy and the BPRD - 1952 #1-5
Hellboy and the BPRD - 1953: The Witch Tree & Rawhead and Bloody Bones
Hellboy and the BPRD - 1953: The Phantom Hand & The Kelpie
Hellboy and the BPRD - 1953: Wandering Souls
Hellboy and the BPRD - 1953: Beyond the Fences #1-3
Hellboy and the BPRD - 1954: Black Sun #1-2
Hellboy and the BPRD - 1954: The Unreasoning Beast
Hellboy - The Nature of the Beast
The Visitor - How and Why He Stayed #1
Hellboy and the BPRD - 1954: Ghost Moon #1-2
Hellboy - The Mirror
Hellboy and the BPRD - 1955: Secret Nature
Hellboy and the BPRD - 1955: Occult Intelligence #1-3
Hellboy and the BPRD - 1955: Burning Season
Hellboy - King Vold
Hellboy - House of the Living Dead
Frankenstein Underground #1-5
Hellboy Gets Married, Parts 1-2
Hellboy - The Coffin Man
Hellboy - The Coffin Man 2: The Rematch
Hellboy versus the Aztec Mummy
Hellboy - Penanggalan
Hellboy - The Crooked Man #1-3
Hellboy - The Corpse
Hellboy - World’s Greatest Paranormal Investigator (short story from Comic Buyer’s Guide #1070)
Hellboy - Double Feature or Evil
Hellboy - Return of the Lambton Worm
Hellboy - The Hydra and the Lion
Hellboy - The Iron Shoes
Hellboy - God Rest Ye Merry
Hellboy - The Troll-Witch
Hellboy - The Baba Yaga
The Visitor - How and Why He Stayed #2
Hellboy - The Sleeping and the Dead #1-2
Hellboy - Heads
Hellboy - Krampusnacht
Hellboy - Mood Swings
BPRD - The Dead Remembered #1-3
The Visitor - How and Why He Stayed #3
Hellboy - Goodbye, Mister Tod
Hellboy - The Last Witch of Fairfield
Abe Sapien - The Drowning #1-5
BPRD - Casualties
Abe Sapien - The Haunted Boy
Hellboy - The Vampire of Prague
Hellboy - The Varcolac
Hellboy in Mexico (most of this occurs in past but the framing sequence occurs here)
Abe Sapien #8
Abe Sapien #30
Abe Sapien - The Abyssal Plain #1-2
Abe Sapien - The Devil Does Not Jest #1-2
Hellboy - The Whittier Legacy
Hellboy - Buster Oakley Gets His Wish
Hellboy - The Bride of Hell
Hellboy - They That Go Down to the Sea in Ships
Hellboy - The Lost Army (Novel)
Hellboy - A Christmas Underground
Hellboy - Dr. Carp’s Experiment
Hellboy - The Dragon Pool (Novel)
Hellboy - The Ghoul
Abe Sapien #23
Hellboy - In the Chapel of Moloch
The Visitor - How and Why He Stayed #4
Abe Sapien - Drums of the Dead
Hellboy - Makoma #1-2
Hellboy - Seed of Destruction #1-4
Hellboy - World’s Greatest Paranormal Investigator (SDCC Comics #2 short story)
Hellboy - The Chained Coffin
Abe Sapien - Subconscious
Hellboy - The Wolves of Saint August
Hellboy - Hi, My Name’s Hellboy
Hellboy - Wake the Devil #1-5 & Epilogue (exclusive to TPB)
Hellboy - Almost Colossus
Abe Sapien - Abe Sapien versus Science
Hellboy - The Bones of Giants (Novel)
Hellboy - The Nuckelavee (prose short story - unsure of exact placement)
Hellboy - The Right Hand of Doom
Hellboy - Box Full of Evil #1-2 & Epilogue (exclusive to TPB)
Hellboy - Being Human
Hellboy - The Promised Smile (prose short story - unsure of exact placement)
Hellboy - Conqueror Worm #1-4 & Epilogue (exclusive to TPB)
The Visitor - How and Why He Stayed #5
BPRD - The Ectoplasmic Man
BPRD (teaser from Dark Horse Extra #42-44)
BPRD - Hollow Earth #1-3
Hellboy - The Third Wish #1-2
BPRD - The Soul of Venice
BPRD - Dark Waters
BPRD - Night Train
BPRD - There’s Something Under My Bed
BPRD - Another Day at the Office
BPRD - Plague of Frogs #1-5
BPRD - Born Again
BPRD - The Dead #1-5
Hellboy - The Island #1-2 & Epilogue (exclusive to TPB)
Hellboy - Into the Silent Sea
BPRD - War on Frogs #2
BPRD - War on Frogs #1
Abe Sapien #15
BPRD - Revival, Parts 1-2
BPRD - The Black Flame #1-6
BPRD - War on Frogs #4
BPRD - The Universal Machine #1-5
BPRD - War on Frogs #3
BPRD - Garden of Souls #1-5
BPRD - Killing Ground #1-5
BPRD - Out of Reach
Hellboy - The Mole
Hellboy - Darkness Calls #1-6 & Epilogues 1-2 (exclusive to TPB)
BPRD - The Warning #1-5
BPRD - The Black Goddess #1-5
BPRD - King of Fear #1-5
Hellboy - The Wild Hunt #1-8
The True History of Lobster Johnson
BPRD - Hell on Earth: New World #1-5
BPRD - Hell on Earth: Seattle
BPRD - Hell on Earth: Gods #1-3
BPRD - Hell on Earth: Monsters #1-2
Hellboy - The Storm #1-3
Hellboy - The Fury #1-3 & Epilogue (exclusive to TPB)
Hellboy in Hell #1-4
BPRD - Hell on Earth: Russia #1-5
BPRD - Hell on Earth: An Unmarked Grave
BPRD - Hell on Earth: The Devil’s Engine #1-3
BPRD - Hell on Earth: The Long Death #1-3
BPRD - Hell on Earth: The Transformation of JH O’Donnell
BPRD - Hell on Earth: The Pickens County Horror #1-2
BPRD - Hell on Earth: Exorcism #1-2
BPRD - Hell on Earth #103-104
BPRD - Hell on Earth: The Return of the Master #1-5
BPRD - Hell on Earth #107-109
BPRD - Hell on Earth #105-106
Abe Sapien #1-7
Hellboy in Hell #5
BPRD - Hell on Earth #110-114
Abe Sapien #9-11
BPRD - Hell on Earth #115-119
Abe Sapien #12-14
Abe Sapien #16-22
Hellboy in Hell #6 & Prologue (exclusive to TPB)
Abe Sapien #24-26
BPRD - Hell on Earth #120-123
Abe Sapien #28-29
BPRD - Hell on Earth #124-129
Abe Sapien #31
BPRD - Hell on Earth #130-132
Hellboy in Hell #7-8
BPRD - Hell on Earth #133-134
Hellboy in Hell - The Exorcist of Vorsk
Abe Sapien #32-33
BPRD - Hell on Earth #135-139
Hellboy in Hell #9
BPRD - Hell on Earth #140-142
Abe Sapien #34-35
Hellboy in Hell #10
BPRD - Hell on Earth #143-147
Abe Sapien #36
Koshchei the Deathless #1-6
BPRD - The Devil You Know #1-6
Abe Sapien #27
BPRD - The Devil You Know #7-10
That should be correct, though I may be wrong with some placements. And that’s only if you want to take the extremely detailed chronological approach. The placements don’t account for flashbacks, of course, but the present day events of those stories occur more or less in this order.
Again, if it’s your first time reading it I wouldn’t necessarily recommend doing it chronologically as some of the earlier stuff can spoil the stuff that comes later, but I’ve done chronological re-reads and it works quite well, especially the overall mythology and character growth/arcs.
Some placements may be wrong so if so please let me know so I can adjust.