Your respiratory system has quite a number of neural and non-neural (e.g., physical, emotional, and chemical factors) controls in addition to the ability to be voluntary controlled.
- A strong influence on much of our respiratory physiology is a response to changes in carbon dioxide in the blood (well, more specifically, it's blood pH that is regulated). Oxygen homeostasis is also controlled.
As a result, the duration you're asking about almost certainly is dependent on total lung capacity, actual volume of air inhaled, diffusion capacities, activity levels, etc. as each of these would determine levels of oxygen and CO2 in the blood and available to tissues (such as the brain).
- In other words, since gas homeostasis plays such a prominent role in respiratory control, the duration of any "reflex" response would vary between person to person (based on their anatomy) and even for an individual person based on circumstances.
Also, I'm not personally familiar with any such reflex that you mention.*
In fact, some children intentionally hold their breath until they pass out! This passing out is actually a useful adaptation because it allows the body to return to using involuntary breathing controls to prevent the child from depriving themselves of oxygen long enough to induce death. Seattle Children's Hospital suggests normal breathing returns in under 2 minutes.
Also see the fainting game that got popular among teens earlier this century that involved intentionally causing self syncope. [WARNING: DON'T BE THIS STUPID]
* If you can update your question with a source or any additional information about the "reflex" you mention, I or someone else might be able to address the reflex or your source of info more specifically.