"accidentally found" is correct and usable in written English.
You could use it when something is found, usually something unexpected and often a coincidence. For example: "I accidentally found an old photograph of my grandmother in an antique shop."
Well, I accidentally found myself on the new KinkBNB website.
They accidentally found themselves in a position of great power over others.
I find it rather odd that this article says that everything that has made the Masters violins were accidentally found.
JENA MALONE leapt into the chauffeur-driven Lincoln Town Car like a colt that had accidentally found itself in Hollywood.
A veritable lynching was perpetrated against two or perhaps three soldiers who accidentally found themselves at a Palestinian police roadblock.
My first enocounter with Information Theory came up when I accidentally found Tom's Stanford University technical report on gambling and its relation to data compression.
When one of Evan's letters to himself is accidentally found on a suicide victim, the victim's family assumes that he was a close friend.
Strolling along one of those dim corridors the V&A is riddled with, I took a turn and accidentally found myself in a spacious private apartment.
We were interested in natural climate variations and accidentally found ourselves once again in the center of the climate change debate because of the implications of our findings.
All those treks through the rain forest paid off, and yet he believes the Vika rat is rare, and in danger of extinction by the same loggers who accidentally found it.
Film-maker Rolf de Heer's staged a similar scene in his 2007 time travel comedy Dr Plonk, when his displaced protagonist accidentally found himself transferring from the silent film era to modern society.
