I contacted about 5 RV parks in the area and only KOA allowed parking, but they were full. I did find a few possible options, though. I ended up not flying out of Boise so I can't tell you much more.
In addition to the ones below, try looking up Boat Storage places. We ended up flying from Seattle and that was how I found storage there.
Boise Riverside RV doesn't have storage, but they suggested that "I would check out the Airport Chevron. They offer a park and fly service and own a lot near our facility."
https://indiancreeksports.com might have some storage.
Ron at KOA said: "I have a friend with a secured RV storage lot that he is renting.
Rick Wintrode (208) 573-9739
Tell him that I referred you."