is it considered good practice to pass callBacks to redux async action?

This would be bi-directional data flow, which breaks the first rule of flux.

The pattern is fine per se. If this is a notification local to the component, feel free to avoid wiring it through Redux.

That said callbacks are completely unnecessary because you are already returning the promise. Just wait for its completion.

this.props.dispatch(asyncAction(item)).then(onSuccess, onFailure);

However if you have many components with such notification bars, it's better to have a reducer keeping the current notification and reacting to actions.

I suggest having separated store named smth like NotificationStore and build notifications infrastructure around it. You can use callbacks, but it's way to big problems in future.