Your calculations are way too complicated. If you have 12mAh of capacity, then with 6 mA load, it will last 2 hours, ideally regardless of power consumption profile. With duty cycle lower than 1, you spread those 2 hours over time. A minute is 60000 ms, and you work for 1 ms out of that time, which means that battery will last proportionally longer, or 60000 * 2 hours.
I don't really follow your math, but where do you factor in 1 ms there?
No need to involve energy here for this basic scenario.