Can i take amoxicillin and severe cold and flu nyquil at same time?

Yes these: medications should not interfere with each other's function in your body. Amoxicillin is also non-sedating while Nyquil usually has some sedative effect. So amoxicillin should not increase the effect of sedation. I am assuming you were prescribed both medications by a healthcare provider and not self-medicating. Either way it should be okay as long as you are not allergic to either of these.