Hi Patch,
I got this from Wikipedia
Flax seeds are chemically stable while whole, and milled flaxseed can be stored at least 4 months at room temperature with minimal or no changes in taste, smell, or chemical markers of rancidity.[4] Ground flaxseed can go rancid at room temperature in as little as one week.[5] Refrigeration and storage in sealed containers will keep ground flax from becoming rancid for even longer.
but I couldn't find any info on cooked flax. Best thing I can suggest is try freezing some and test them after, say, a month.