Green oak will shrink and move a lot more than dried oak. With windows you want to limit the movement as much as possible. Kiln dried will be less likely to break the glass or open up gaps. The downside is that dried oak is nort as easy to work.
It also depend on what section timber you wish to use you will struggle to find truly dry (read 10 or 12 percent ) oak in section more than 3 inch so you would need to do some laminating.
If it's a window frame that's catching the weather externally, then you might even find that well air dried stock will be better behaved than kilned Oak that may have been rushed.