Have Oak wood that is dried to 6 %. Have made exterior shutters. Put a coat of Kiltz primer and 2 coats of Semi-Gloss latex house paint. A brown streak came to the surface and continued to get worse as days past. Put a final coat of Kiltz Flat exterior paint and the streaks still came through. Left shutters out overnight and they had a puddle of brown moisture on them which rinsed off.
How can I seal these shutters so that the streaks do not keep coming through?

First why did you use oak for this, problem one lol. Cedar or redwood, or other forms of pine work much better, even cypris is a staple wood and is great outside.

Never the less right now sealing it may not work for now till the wood is done, if you try and seal it now it may start to bubble or blister. As to how to get the moisture out I really don't know other than let it do what it will and just wait till it stops. I know they make systems to dry wood but you wouldn't have access to something like that. Maybe just use some kilz again, try and use the oil base version of kilz it is much better for this than laytex. Id start there. Good luck