This would be a first for me, so advice and warnings are greatly appreciated!
Are there perks I should be asking for? Are the 'red flags' that I should watch out for?
If you are working with others the first thing I would personally ask is what they use for communication (slack, IRC, e-mail, etc). If you are going to be part of a team where the majority of them work in an office it is very easy to be forgotten about or left out of things depending on what technology they are using and what the culture is.
I would also ask what the work hour expectations are and have it documented. Are you expected to be online from say 8am-5pm local time? I have seen some people told "just make sure you get your work done" but then let go because they were not making themselves available during the hours the rest of the team was online (even though their work was getting done).
In my experience perception plays a big role in working remotely. If the people in the office don't constantly hear from you or see you online the idea that you are slacking off because nobody is there to manage you starts creeping in.
Also don't be afraid to ask for the same type of perks non-remote employees get with regards to hardware/software/etc.
Does the company already have a good system in place for remote collaboration, e.g. Slack channels for asynchronous standups, shared calendars, Confluence documentation, screen sharing tools for pairing, Google Hangouts, a healthy PR and code review process? Those tools and processes will need to be habitual for you to be a productive member of the team.
The trickiest component of remote work is communication. Ask other team members how they collaborate effectively and the tools used to do so.
Working from home is a perk in itself but its not for everyone. Sometimes I find myself going into the office just to get out of the house.
Edit: Also, a lot of remote employers will want to meet face to face eventually. Make sure they offer to compensate for travel expenses and a clear duration in the terms.
I'm going to operate under the assumption that you're a remote worker applying for a job that involves working with in-office folks since that wasn't provided in the question and it's the only thing I have experience with. There are a few things I would recommend discussing/negotiating before choosing to take the job.
Make sure that the company is going to provide you with the equipment, appropriate software licenses and such that you need to do your job (or salary for you to afford the expense). Consider things like upgrade frequency, office supplies and other factors that are normally a given in an in-the-office job.
Discuss communication expectations and work/life balance. What communications tools does the team use? Are they appropriate for asynchronous communications or is the culture one of "tap the guy on the shoulder"? There's a sort of undercurrent of concern that rips through you when you're a remote worker that might have you feeling like you have to work "all the time", especially if your team is in a radically different time zone. Prior to accepting the job I ensured that my performance would be based on meeting project deadlines with appropriate requirements to be in meetings when they're scheduled (and none are scheduled at obscene hours of the night for me). My biggest concern was that being the guy not in the office would equate a perception of being the guy who is just taking a vacation or goofing off (those who know me would laugh at that because I love the work I do, however, I tend to work a lot from a family vacation home, so the appearance was a concern of mine). I write software and my most efficient times to work vary. Knowing that often I can get 14 hours worth of normal work done in 6 hours if I target doing it at the right time, I wanted that flexibility to be baked into my work contract. Provided my scheduling flexibility doesn't block the rest of the team (it doesn't due to unique circumstances of my job), or cause me to miss a deadline (it often results in me being early, instead), I'm free to work when I want and due to the added efficiency, that equates to hours/week of time that I get back.
The bottom line on that last point is be sure to have a very solid discussion on how your performance will be tracked. Aim for the most objective measurements you can get, and ensure that you have substantial input in deciding deadlines. There's always external pressure on deadlines, but if you can't be a prime component in that decision making process you run the risk of being given work that is not possible to complete on time, setting yourself up for failure. If your discussion is dismissed or the answer is "we'll figure it out", beware. Your manager is likely the kind who equates performance with "butts in chairs" and you will always be an empty chair.