Games like Don't Flee
Games like Don't Flee include Escape the Backrooms, Poppy Playtime, The Exit 8, Buckshot Roulette, and Layers of Fear (2016). We matched them by the tags players give Don't Flee on Steam (Horror, Psychological Horror, Exploration, First-Person, and Singleplayer): closest matches first, and among equally close ones the better-known games.

Escape the Backrooms
Shared: Horror · Psychological Horror · First-Person

Poppy Playtime
Shared: Horror · Singleplayer · First-Person

The Exit 8
Shared: Exploration · Horror · Psychological Horror

Buckshot Roulette
Shared: Horror · First-Person · Singleplayer

Layers of Fear (2016)
Shared: Horror · Psychological Horror · First-Person

MiSide
Shared: Psychological Horror · Horror · First-Person

Garten of Banban
Shared: Horror · Psychological Horror · First-Person

Five Nights at Freddy's: Security Breach
Shared: Horror · Singleplayer · First-Person

SOMA
Shared: Horror · Psychological Horror · Exploration

Lethal Company
Shared: Horror · First-Person · Exploration

Outlast
Shared: Horror · First-Person · Psychological Horror

SILENT HILL: Townfall
Shared: Horror · Psychological Horror · First-Person

Resident Evil 7 Biohazard
Shared: Horror · First-Person · Singleplayer

Amnesia: Rebirth
Shared: First-Person · Horror · Singleplayer

Scanner Sombre
Shared: Horror · Exploration · Psychological Horror

In Sound Mind
Shared: Horror · Psychological Horror · Singleplayer

Inside the Backrooms
Shared: Horror · Psychological Horror · Exploration

Platform 8
Shared: Psychological Horror · Exploration · Hidden Object

Backrooms: Escape Together
Shared: Horror · Psychological Horror · First-Person

Superliminal
Shared: First-Person · Psychological · Singleplayer

Still Wakes the Deep
Shared: Horror · Psychological Horror · First-Person

September 7th
Shared: Horror · Exploration · Psychological Horror

Mouthwashing
Shared: Horror · Psychological Horror · Psychological

Little Nightmares II
Shared: Horror · Singleplayer · Psychological Horror