Why would recessed ceiling lighting blink occasionally? Dangerous?

Most likely a poor connectioon at the switch or power supply. The wires going to the switch are they around screws or back stabbed?

If they go off for a few minutes, then back on, The thermals in the cans can open until they cool down, usually from over wattage bulbs.

I think we both forgot to answer your second question, yes, can be dangerous

I also missed in unison, which would eleminate the possibility of thermals?