The Kionix company does not appear to be heavily involved with machine condition monitoring applications. All of the triaxial accelerometers on their website appear to be labeled "not for new designs". The accelerometer you have appears to be an old design. There are better performing MEMS accelerometers on the market, such as available from Analog Devices that have considerably lower noise.
There is no "best practice" for low-speed bearing vibration measurements that I'm aware of. There are plenty of vibration monitoring pitfalls that could cause false alarms or no fault detection at all until complete failure occurs; based on reasons previously mentioned. The accelerometer choice is important, but the real challenge can be finding a suitable signal analysis method including overall levels, waveform, and spectrum. I cannot confirm if the product you have will provide an adequate warning prior to the shaft stops rotating or visible smoke appears!
"or install one of the old "earthquake switch" devices on it to indicate a problem" This total piece of junk for this application!!