That's funny! Question is - is the cat swishing oil, gold fish or parakeets?
You can find flax seed oil at any healthfood store. Make sure it's refrigerated and that you keep it in the fridge. It goes rancid very quickly if left at room temperature. Barleans is the best brand IMO.
Just a warning, I notice that women don't seem to like the taste of flax seed as much as men. Most of the other flax seed swishers on the board seem like they've been guys.