I'm wondering if it would be possible/hard to do beaconing for an indoor location system using https://tinycircuits.com/collections/communication/products/bluetooth-low-energy-tinyshield as the bluetooth radio.

I'd imagine there must be some way to scan for nearby bluetooth devices, read their rssi, and use that to triangulate where a given device is located. Does anyone have some code to do this?

Well, it is technically not that challenging to find a list of devices in range and compare signal strength. But, that wouldn't help you do anything very accurate nor reliable, particularly indoors. You would need to know the accurate fixed positions of several (more than 3) beacons in range at any given moment.

That would still only put you in the ballpark because signal strength is not a reliable metric of distance indoors. The only way I can think of to calibrate this would be to take several measurements at several locations to get a sort of portrait of what readings are typical of a given location. Then, when trying to locate the device, you would find the portrait that best matches the current readings.

You could improve on that by getting sophisticated by tracking the movement of the device to help predict where the device is most likely to be. This would help by filtering out locations that the device is unlikely to be at, even though the readings may otherwise be a good match.