Yeah, get the trailer tires off the concrete. I don't like plywood because of the glue used to hold it together, so I use plain old pine lumber. A piece of 2x8 about 6 feet long for each side is easy to back onto. 2x10 or 2x12 would be even easier to back onto. And even on the lumber, you still need to jack up the trailer a bit to get most of the weight of the trailer off the tires. On my 5er with electric front jacks, with the trailer slightly down in front, I'd put the rear stabilizer jacks down firmly, then jack up the front until the trailer was level. No need to get the tires off the wood, but at least take some of the weight off the tires.
And UV is the tire killer, so cover the tires with something that will allow zero sunlight to hit the tires, without trapping water vapor inside the cover. Unbreathable plastic cover is not good, so use a more-expensive tire cover that can breathe air, so the water vapor goes away.
If the trailer is in storage for several months, drive very slowly for a mile or so, then gradually increase speed until the tires begin to warm up. That will get rid of any flat spot without damaging the tire. That's especially important if your tires are bias ply. You can recognize bias ply trailer tires because they won't have an "R" in the tire size, such as radial size ST225/75R15. Instead the bias ply tire size will probably contain a "D", such as ST225/75D15.
Grumpy ole man with over 50 years towing experience. Now my heaviest trailer is a 7,000-pound enclosed cargo trailer, RV is a 5,600 pound Skyline Nomad Joey 196S, and my tow vehicle is a 2012 F-150 EcoBoost SuperCrew.