Please note that this is not the Flatland story, but it may have referenced it.
I recall reading a different story about a programmer writing a virtual two dimensional world simulation, which then starts glitching because it manages to synchronize with an actual living two dimensional being.
The story then relates the account of that being and his life fishing, and living in underground houses through a series of conversations or descriptions between the human and the throg(?) / throc(?)
Eventually the two dimensional being meets a sage from their world who teaches them how to perceive the third dimension, and he leaves his world, at which point the connection to the humans computer program is severed.
The human tries to run the simulation again, but in vain, as it just behaves normally and never glitches again.
This story was probably in the 80's? Though it may have been published earlier.