How do I get a job as a headphone reviewer?

You can just contact the publisher/editor via email for sites like Soundstage, Part Time Audiophile, Stereonews.net, etc. and tell them you’re interested in reviewing headphones and a bit about your audio experience/equipment.  They’ll probably ask for a writing sample, or in my case they just had me write a review of one of my components and that’s how I got started.  Hope this helps, and best of luck.

Do it for free and attract a following is how social media works today.  

With academia, I would write something related to my discipline and then follow the submission guidelines for whatever periodical I wanted to be published in. So I would think you could do a review and then contact Stereophile or whoever and tell them you’re interested in sending them your work for publication and ask them for instructions on how this is done. Every periodical might have a different set of guidelines. Some editors may welcome these types of entries and some may not. I would not write a review and then just send it in to the magazine to see how they respond because administrative staff will object to this and it could ruin your chances to publish with them altogether.

I was thinking about your question and realized that headphone reviews are all about the equipment you to drive them. So, I went to see your virtual system. Surprisingly, there isn’t one. I would start there. Let’s see it and maybe a summary of how you developed it and your history. Sounds like you have heard quite a few.. 
 

I’ve used headphones extensively since the ‘80s, and particularly over the last twenty years while putting together a good headphone system. I found the sound of headphones vary greatly depending on the equipment you use to feed them. I have gone through over half a dozen carefully chosen good quality headphone amps and found that the strengths and weaknesses of different headphones can vary tremendously depending on the headamp… the amount of detail and more subtle tonal balance is strongly varies be the source / DAC. Have you found the same?
 

I guess if I were to try doing reviews I would want at least one high end system and a couple that are more common ones. I noticed that differences between headphones ( I have a bunch, I’m sure you do as well) that seem big with less than ideal input nearly disappear when fed a really high current natural sounding input. 
 

Sounds like you are ideally suited skill wise I’m looking forward to hearing more about your interest in headphone systems.

If I were you would go to head-fi.org and take a look around if you haven’t done that already. Headphones dedicated site that often times ask for reviewers, mostly voluntary, but still get you a foot in the door. Hope that helps.

@ghdprentice I may not have as much experience as you think, given that I only had two periods in which I updated my system and it stayed the same for up to seven years in-between. In the last period of update, I discovered a technician in the New Jersey Audio Society who does great custom work, and ended up with fairly inexpensive stuff that was custom worked over. For example, I have a Bravo headphone amp from 7 years ago... cheap Chinese junk, right? ... with all the parts replaced, shielding and damping added, beefy linear power supply, that sounds fantastic.  My current DAC, Windows 10 computer, all cabling, power conditioning, etc. is custom modified by this guy. So this wouldn't be a good starting point for a review as no one can compare to it. My current best headphone is a pre-fazor LCD-2 with a custom cable soldered directly to the drivers. I've heard fazor LCD-3's and LCD-X's but liked mine better. But that was the last time I was tweaking my system. I haven't heard any new headphones since.

I'm starting a new period of system upheaval, focused mainly on the DAC and transport, but it's getting expensive. I can't sell my custom modified stuff to pay for it.

So writing reviews may not be the best idea at this point. I can't justify spending a lot of money in order to make a little money. I suppose even the giants of speaker system reviews who get sent free equipment, etc.  are using their homes, an enormous expense they paid for themselves, to provide a base for doing the review.

Wait... tax deductibility! Well, not quite enough to make it practical.

Thanks for everyone's ideas.

Yeah, you have to watch out for those system upheavals… they can be costly. Last time it happened with me it cost about $10K for my headphone system. That sounds bad… but unfortunately then comparing it to my main system I realized I needed to upgrade my main system… that cost $70K. Don’t get me wrong, it was all absolutely worth it… but once started it can be hard to stop.