Will the alcohol in breath mints and mouthwash cause nausea if I am taking flagyl?

Not usually. There is such a small amount of alcohol in mints you should not have a problem. Mouthwash usually does contain alcohol, but you should be fine as long as you don't swallow it. I wouldn't worry about it.
No. You are correct that you should not drink alcohol when using Metronidazole (flagyl). The small amount of alcohol in a breath mint would not be enough to trigger a reaction.