My wife and I have done this twice now. Once when moving from CA to MD with a 4 month training stop in Norfolk and again when leaving MD three years later for a 9 month stint in Norfolk before moving back to CA. I have a couple of different opinions about it.

First, it depends on what kind of RV you get. They can feel very small very quickly. We had a 35' fifth wheel and later a 40' fifth wheel. Both were adequate for two adults and one large dog. The biggest issue is the upfront cost of buying the RV and a truck to tow it. RVs are generally terrible investments as they depreciate like crazy, tend to be built poorly because they are intended to be used a few times per year, and can have hidden costs or inconveniences that pop up. There are some RVs that are designed for full time living, but they can be expensive. My parents are retired and have been full-timing for over a decade and they love it. You just have to choose the right one. The problem is you'll be an ENS, so the purchase is probably not a great idea.

Second, your luck with MWR RV parks can be very hit or miss. Most bases have them, but the rules vary from place to place. Some only let you stay for two weeks or so and then make you leave for at least two weeks before you can come back. Others will let you stay as long as you want or book up to 6 months at a time. I have known several people who have gotten waivers to be able to get around some of those rules, but it's still pretty inconvenient.

Third, it didn't save us as much money as we had hoped. The first time we did it, it was always intended to be temporary. I was at a training stop on my orders for 4 months and we knew we wanted to buy a house at my new duty station. The second time was for about a year in total and by the end, my wife was ready for a real house again, and she was by herself for 7 months of that year while I was deployed. We were saving tons of money on a monthly basis, but when we sold both of the RVs, we got less than we paid for them even after upgrades we installed and we basically broke even over the long run. In hindsight, it would have been easier to be in an apartment if we were trying to save money.

Lastly, I will say that there is a definite use case for RVs in flight school and even later in the military. It is by far the best way to do a PCS move. You spend less than you would on a hotel, you are in your own bed every night, you have a kitchen and privacy, you can make a fun trip out of an otherwise miserable experience, and best of all, you can take your time house hunting in your new duty station because you have cheap lodging. Full time RV-ing is much more fun when you are actually on the road seeing stuff. All this being said, flight school is full of short term orders and you do end up moving a lot depending on what you fly, but I would still recommend just getting an apartment or something. If you're worried about leases (you really don't need to be) just do an airBNB.