A buddy of mine worked as a security guard and he wasn't allowed to have anything at all with C or D batteries and no light longer than a certain length. Years ago someone else working as a security guard with the same outfit beat a perpetrator with a 4D mag really bad and they got taken to court and the company put a limit on flashlights. I assume it's similar for the police.
Thankfully there are no state regulations for security officers. At least not in New York. What you can carry depends on the regulations set forth by whichever private security company you work for
or whatever individual rules the client hiring the company sets forth. Indeed, some have very strict regulations/rules. Such as nothing over a 2C Maglite in terms of size. Others are even more strict. Such as no metal bodied flashlights at all. (Those may or may not put restricts on length and size.)
Meanwhile other companies and clients may have absolutely zero restrictions in place. That's been my situation for the past four years. Just a few days back, I brought a vintage 6C Maglite to work to modify it during my break, and test it out during my foot-patrol of the large parking lots the client has. I left it sitting on top of the front desk while checking the monitors as numerous folks walked by to head home. No one batted an eye, no one said anything. There's a camera pointed at the front desk. And the client's representatives can access it from a laptop at their home. I never got called in, never questioned about it. And I knew it wouldn't be an issue.
Now, obviously, if something happened that was similar to what that individual did with the 4D Maglite, I'm sure major restrictions and policy changes would be put into place. But right now, no one cares.
I'd like to think the NYPD has official policy in place about flashlights being bright enough to get the job done, with runtimes lasting the length of an entire shift. But honestly not sure about that.