No. You don't want copper mixing bowls; you only think you do because copper is so pretty. Copper is a wonderful conductor of heat, which is why it is the cookware of choice for so many cooks. But copper by itself is toxic and tends to leach into most foods, which is why copper cookware is lined (traditionally) with tin or (more often nowadays) with stainless steel.

The only unlined copper vessels on the market are bowls, which enhance the whipping of egg whites (and which are essentially always round on the bottom to facilitate whisking), and polenta pots, zabaglione (or sabayon) pots, preserves pans, and sugar pots. These bowls and pots are either so seldom used that they pose little risk, or they do not react with the foods for which they are intended.

Whether or not you would be exposed to much risk if you used an unlined copper mixing bowl in your day-to-day cooking, we haven't been able to come across any with flat bottoms. We can point you toward a set of round-bottomed copper bowls for beating egg whites and beautifully displaying fruit in your kitchen, or a rubber-coated flat-bottomed stainless-steel mixing bowl, or a lovely blue set of Emile Henry ceramic mixing bowls for day-to-day use. But not, unfortunately, a set of flat bottomed copper mixing bowls.