How the Kv rating relates to power generation with BLDC motors
For a BLDC, Kv is based on half of the peak-to-peak voltage. In other words, it is based on the amplitude of the sine-wave voltage. The units of Kv are rpm/Volt.

So to measure it, spin the motor at a known RPM, and measure the amplitude of the phase-to-phase voltage. So let's say you measure the voltage and it is 10V peak-to-peak, or 5V in amplitude. Let's say the motor is spinning at 1000 RPM. Then the Kv is 1000 RPM / 5V = 200.

This measurement is done when the current in the windings is zero. If you are using the motor as a generator, then the output voltage will be lower than the Kv predicts due to resistive losses in the copper windings. If you are driving the motor, the phase-to-phase voltage will be higher than the Kv predicts also due to resistive losses in the motor windings.

The wikipedia page on motor constants can be used as a reference, however I have experience measuring motor Kv to compare with manufacturer specifications.

https://en.wikipedia.org/wiki/Motor_constants#Motor_velocity_constant,_back_EMF_constant

In your example, you say you are spinning at 1000rpm and the Kv is 1000rpm/V. So you take 1000 rpm and divide by 1000 rpm/V and the result is 1V.

Note: that is not the RMS voltage. It is the peak voltage of the sine wave, which is also half of the peak-to-peak voltage.