Are will it be ok?
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The danger of orange oil to birds is a real danger, but a very minimal one; the EPA states it is a minimal risk.
I don't know what brand of food you feed your parakeet. We use McBride's. Different bird seeds are a host to a hugely varying list of ingredients. Ours doesn't have any orange oil in it because yes, it's toxic to them. The amount that is in *some* parakeet seed is "minimal risk" according to the EPA, but to be honest with you - minimal risk ingredients shouldn't be placed in there at all. There's also Xylitol in some dog foods, dog toothpastes, dog treats, dog chews and other canine products (and it's been proven to actually be deadly to dogs, nothing close to orange oil against bird).
If I were you - I wouldn't give the orange oil parakeet seed to your parakeet.
They place orange oil in *wild* bird seed to attract flies on purpose - to draw in the birds to your birdfeeder that eat buggies (IE: warblers, tanagers and woodpeckers). Some of the same manufacturers also produce parakeet seed and the orange oil is already in batch production for the other seed so they don't bother separating the two for what is best for the particular bird.
At any rate - the risk is minimal to both your chickens and your parakeet and the chances of it affecting either one are very small - but because that risk is there, if it were me, I'd toss the affected feed.
[edited to add] PS - I do highly recommend McBride's parakeet food. :] (for your parakeet not the chickens, hehe)