What I will say is that it makes it much easier on the Admin CM if squads flip-flop each frame. It also offers a better opportunity for the opportunity to fly a requested side for a specific FSO, in case you want to fly a specific ride. I'll describe that below. Remember that FSO is about having fun and not about having the best ride.
Typically, most people that request Axis for my FSO's will get it, as most of the time I have too many Allied requests. On the other hand, I will honor as many Allied requests as I can. When I need to give a squad a side they didn't request (which typically means squads that request Allies when I need to fill empty Axis squad slots), I start with the squads that (1) haven't updated their registration and (2) have flown Allies in succesive FSO's, in that order of priority.
One thing that flip-flopping offers a squad is a better chance to fly their favorite ride. If a squad flies Allied, for example, for two months in a row, and then, in the third month, their favorite allied ride appears in the planeset, they have almost no chance of flying it. If however they have flown both Axis and Allied sides equally in the past, and they happen to request the same side two times in a row in order to fly their favorite plane, I see that they have made an effort to contribute to both sides, and have a much easier time assigning them as requested.
Another bit of advice: If you see a plane-set in an FSO that doesn't offer your favorite ride, my advice is to consider flying the opposite side, so that the next month, if your favorite ride is in the planeset, you can easily make a case to be included on the side of your choice. For example, my squad favors the P-47. If its a Eastern Front setup, I have no problem flying German because we don't have the opportunity to fly the Jug. If its a Pacific naval setup, I don't mind flying the Japanese because we don't have the opportunity to fly the Jug. When that magical setup comes along that includes the Jug, we can make a pretty good case to be included as an Allied squad since we've been voluntarily flying both sides routinely.
That being said, for next month's FSO, for you squads that maintain an Axis focus, especially those squads that favor Germans rides, you'll have your shot at flying German, regardless of your past few FSO's. I won't penalize you for consistently volunteering to fly Axis just because we will, presumably, have a lot of squads requesting Axis.
Finally, I'll caveat this all by saying that ultimately, it all comes down to the needs of the Admin CM. If he needs 10 squads that requested Allied to fly Axis, that's what he'll do and vice-versa. But, should you be assigned Axis, and you're an Allied-centric squad, show up with the same numbers you always do. If you're assigned Allied, and you're an Axis-centric squad, show up with the same numbers you always do. The same goes for type-rides as assigned by the CIC. If you're a fighter-centric squad and you get assigned bombers, meet your commitment, and vice-versa. To not participate when you don't get your favorite side or ride is bad FSO ettiquette.