Couple of thoughts.

Red oak doesn't handle being wet very well. If these posts tend to get wet often, white oak would be the better choice.

Shrinkage depends on the moisture content at installation and, to a lesser degree, on whether these posts get much direct sun or are always shaded. "Uncured" isn't nearly specific enough to make predictions. If the wood is freshly cut and soaking wet, shrinkage will be considerable. If it's been stacked outdoors for several months, shrinkage may be negligible.

I am planning to use White oak, seems to be a little more rot resistant.

The boards will be freshly cut, though I don't know how long the logs have been sitting at the mill. There will be very little direct sun exposure. Should I stack the lumber on the porch for a few weeks prior to installation?

A lot depends on how everything will be put together, but building with green wood is a very dicey proposition. The wood will shrink considerably as it dries, joints may partially disassemble themselves, etc. A flatsawn white oak board that starts out at 8" wide when wet will shrink to around 7.5" before it stabilizes.

A few weeks of sitting on the porch is not enough to save you from this issue. Fresh sawn, the wood will be sopping wet. Half of its weight might be water. Much of that water will evaporate in those few weeks on the porch, but the shrinkage won't even start until the moisture content gets below 30%, by which point drying will slow considerably. FWIW, a common rule of thumb is that air drying lumber takes about a year per inch of thickness.

In short, I wouldn't do what you're thinking of doing.