This list, though extensive, is in no way exhaustive. Many literary journals will consider short prose whether they advertise that fact or not. But these links lead to journals that have expressed a specific interest:
A3 ReviewArts & LettersAtlas + AliceAtticus Review
Baltimore ReviewBarren MagazineBending GenresBooth ReviewBurningwood Literary
Catholic Digest “Last Word” essays Cheap PopCincinnati Review (micro contest)Citron ReviewCleaverConstructionCraft LiteraryCutbank
decomPDeep Wild JournalDefunctDiagram
Ellipsis ZineEmpty House Press
Fairy Tale ReviewFeedFIVE:2:ONEFoliate OakFugue
Gigantic SequinsGordon Square ReviewGuernica (fewer than 2,500)Gulf Coast
HippocampusHobartHumana Obscura (nature focused)
Long Leaf ReviewLost BalloonLunch Ticket
mac(ro)micMatchbookMonkeybicycleMoonPark ReviewMslexia (UK based; “for women who write”)Multiplicity
New Delta ReviewNew South JournalNew Orleans ReviewNY Times Modern Love (a bit longer, 1500-1700 words)
Paper DartsParhelionPassages NorthPidgeonholesPithead ChapelPorter House ReviewProximity
RedividerRiver Teeth (Beautiful Things)Sidereal MagazineSleet MagazineSmokelong QuarterlySonora ReviewSplit LipSpry LitStonecrop ReviewSundog LitSweet: A Literary Confection
Tahoma Literary ReviewThe Adroit JournalThe Christian Science Monitor’s “Home Forum” sectionThe CollagistThe Curator (Essays that contemplate the stories behind everyday objects)The Florida ReviewThe ForgeThe NasionaThe OffingThe Pinch JournalThe Real StoryThe Schuylkill Valley JournalThe Sun’s “Readers Write” sectionThorn LiteraryThreadThreadcountTriQuarterly Online
Unbroken JournalUnder the Gum Tree
WaxwingWildnessWOW! Women on Writing
___Further Resources
The Best of Brevity: Twenty Groundbreaking Years of Flash Nonfiction
The Rose Metal Press Field Guide to Writing Flash Nonfiction
The Brevity Blog: Tips, Craft Discussions, Contest Announcements, and Essays on the Writing Life
“Flash Nonfiction: An Interview with Dinty W. Moore” (River Teeth blog)
Literary Magazines and Journals Database (from Poets & Writers; filter by “creative nonfiction”