It may not make any difference, but the structural integrity of the shutters and how straight-grained all the wood is may make drying flat preferable if you can arrange it somehow. I would do this myself given the chance, just to be on the safe side.
Stacking them on the ground is probably sufficient (the bottom one not in contact with it) but if they can be supported higher up on sawhorses, an old bench, some old chairs all the better.
If on the ground raise the bottom one on some bricks, a couple of lengths of 2x4, something.
If using 2x4s the bottom shutter can go directly on them, if using bricks/sawhorses/bench/chairs you can protect them and/or it with a few layers of newspaper before placing first shutter1.
Then build your stack, using thin strips of wood in between the shutters to ensure airflow. And final step, place heavy weight on top to counteract any tendency they might have to warp (there may be none, this is just an insurance policy). You can use concrete blocks, stacks of bricks, buckets/old paint tins full of damp sand, weight-training weights or whatever for the weight, but any metal should not be directly in contact with the top shutter.
Now leave them for a week or longer. A few days might be enough, but I'd wait at least a week to be on the safe side and longer won't hurt2.
This is similar to how planks are stickered when air-drying if you're having trouble visualising it.
1 There may be some slight transfer of printing to the wood but this won't matter, regardless of whether you intend to use a clear finish instead of repainting, because some sanding is absolutely guaranteed to be needed and this should easily take care of it.
2 It won't hurt to leave them stacked this way for an extended period, so don't worry if life gets in the way and they get ignored or forgotten about for some weeks.