Diamons will burn at 690°C in pure oxygen. Houses burn at around 590°C. Maybe if you rupture an O₂ tank in a house fire right next to the diamond battery you could pull it off.
I wouldn't worry about small diamond batteries. There is already 1 part per trillion carbon 14 in you. The odd telemetry battery that gets caught in an oxygen fire isn't going to shift the scales much.
A pure oxygen atmosphere is pushing it too much, isn't it?
Anything you have at home, except for the concrete walls and glass will burn in less than 0°C in a pure oxygen atmosphere. A pure O2 tank in a house would be a serious cause of concern.
I wouldn't worry about small diamond batteries. There is already 1 part per trillion carbon 14 in you. The odd telemetry battery that gets caught in an oxygen fire isn't going to shift the scales much.