Flex can be anything from a .1% below TOGA power to (as rudderrat says) climb power. As you don't know where you are in the scheme of things the 10 min limit applies.
Say you happened to use 12 in order to 'save life', I doubt anyone would have an issue. If you used it to give yourself a warm fuzzy feeling then I would suspect that you would be walking...
Just remember, just because it is certified to do it, doesn't mean (for instance) that you should. The 'good' engine, for example, might have also swallowed a bird and lowering its stress levels may be wise.