What advice would you give to a married gay couple looking to possibly explore non-monogamy?
Great question! I have the same advice for you as I do for any person or couple looking to explore a non-monogamous relationship or arrangement: be sure you know what you're getting yourself into.
Now, I recognize you can't fully know until you try it, but there are some hints that it might or might not be a good fit for you. In your case, since you are currently in a monogamous relationship, the #1 thing to ask yourselves is why. If you are going along with the idea to please your partner, or you're attempting to convince a reluctant partner, that's not a good sign.
I myself have never been in a non-monogamous relationship because I find the idea completely unappealing - it doesn't suit me personally because if I like someone enough to want to be with them, I don't want anyone else. (I'm single minded that way.) So beyond any concerns about jealousy or STI's or anything like that, for me it's a non-starter.
Of the people I know who have had positive experiences with non-monogamy, those people have been the "unicorns" dating one or both people in a committed relationship. Being the 3rd (or the 4th, 5th...) I think would be leaps and bounds easier than sharing your partner with someone new.
If you've thought all this through and you are both confident in your reasons for doing it, I would still urge you to proceed with caution. Establish clear rules - sex only, or full on dating another person? Is it something you do as a couple, or as individuals? Do you have a full disclosure policy or a "don't ask, don't tell" policy? What rules do you have about protection, or particular sex acts, number of partners or frequency of encounters? Do you decide as a couple on potential sex partners or is it a unilateral decision?
All of those things should be decided upon and agreed to upfront.
Last thing I should say - I know that there are many non-monogamous relationships out there that work great for some. Monogamy certainly is no guarantee of happiness or compatibility. But it is a framework that most of us are familiar with, and switching gears once you've began a relationship based on monogamy is bound to be very challenging for most.
You might be the exceptions! Keep those lines of communication open and reserve the right to change your mind if your exploration doesn't go as well as hoped. Best of luck to you both!