Hi Slegtvalk. Looks like the Orion stories are in order of publication. There are different interpretations of the chronological order of the tales.
This is Joe Marek's proposal:
"The Hyborian Age, Part One"
"Cimmeria" (poem)
"The Frost Giant's Daughter"
"The Tower of the Elephant"
"The Hall of the Dead" (fragment)
"The God in the Bowl"
"Rogues in the House"
"The Hand of Nergal" (fragment)
"Black Colossus"
"Queen of the Black Coast"
"The Snout in the Dark" (fragment)
"Shadows in the Moonlight"
"A Witch Shall Be Born"
"Shadows in Zamboula"
"Xuthal of the Dusk"
"The Devil in Iron"
"The People of the Black Circle"
"Drums of Tombalku" (fragment)
"The Vale of Lost Women"
"The Pool of the Black One"
"Red Nails"
"The Teeth of Gwahlur"
"Beyond the Black River"
"The Black Stranger"
"Wolves Beyond the Border" (fragment)
"The Phoenix on the Sword"
"The Scarlet Citadel"
"The Hour of the Dragon"
"The Hyborian Age, Part Two"
This is Dale Rippke's
"The Frost Giant's Daughter"
"The God in the Bowl"
"The Tower of the Elephant"
"The Hall of the Dead" (synopsis)
"Rogues in the House"
"The Hand of Nergal" (fragment)
"Black Colossus"
"Shadows in the Moonlight"
"Queen of the Black Coast"
"The Snout in the Dark" (fragment)
"The Slithering Shadow"
"A Witch Shall Be Born"
"The Devil in Iron"
"The People of the Black Circle"
"Shadows in Zamboula"
"Drums of Tombalku" (fragment)
"The Vale of Lost Women"
"The Pool of the Black One"
"Beyond the Black River"
"The Black Stranger"
"Red Nails"
"Jewels of Gwahlur"
"Wolves Beyond the Border" (fragment)
"The Phoenix on the Sword"
"The Scarlet Citadel"
"The Hour of the Dragon"
The very first one, and the only version to be seen by Howard is in the essay 'A Probable Outline of Conan's Career' (1936) by P. Schuyler Miller and John D. Clark, but this only includes tales published at that time. It can be found here:
link