I'm just going to wing it here and say, just wait until you have a new beer ready to inoculate. Take the wood out of the finished Flanders and drop it directly into the new batch. Since the Flanders/sours can sit on the wood for weeks/months/years just wait to keg or bottle until you have a new batch ready for the wood. The safest way to store the oak is IN beer.
Just a though. I haven't actually gotten there yet...

PFC BN Army - Tactical Hop Command
Fermenting - Kolsch, Blonde Ale
Kegged: Flanders Brown
Aging: Brown Lambic, Chocolate Porter
President and Chief Bottle Washer - HopRunner Brewing~Ross