No, you cannot flip your camera to change the mirroring in StreamYard. We originally designed it this way so that all text shows up in your stream correctly, instead of backwards. We understand not everyone likes using their camera this way, so this is a feature we plan to add in the future!
As a work-around, you can check with your webcam company to see if they offer software that you can download to make changes to your webcam. Alternatively, you can use a virtual camera and bring this into StreamYard (note, this is advanced).