That's a hard question. First, remember that we measure hot lumber in the kiln and cold lumber at the planner and just the temperature change may impact the result. Also, as wood cools and sits, the moisture gradient inside the wood may change and a meter may respond differently. The outside temperature and humidity will affect this. How much wind blows through the stack probably affects the change. Also, the final moisture content. If you are drying alder to 8%, it will probably change less than hemlock dried to 17%.
To actually answer the question, maybe a couple percent.
If you really want to find out, meter in exactly the same locations and see how much the loss is. Alternatively, if your mill has the capability, weigh a unit right after shut down and a day later. You could weigh a few boards, but you need a pretty good scale (+/- 1/2 to 1% of board weight resolution, a bathroom scale probably won't work).
For dry lumber (say 7% for flooring or furniture) you might see a MC increase.
Keep in mind the important thing is to do a hot check in exactly the same way every time and pull the load so that the wood is at the correct MC when it hits the planer (I know it's not easy). Meaure in the same locations, handle the meter in the same way, use the same meter settings etc. to make the process as repeatable as possible. Same for an in-kiln meter. If the hot check is 19% to get the lumber through the planer at 15%, then pull at 19% instead of worrying too much about why there's a difference. In-kiln meters can usually be adjusted following the manufacturer's instructions.
Maybe other people can comment on the levels at which they pull the load compared to what they see at the planer.