Think about tilting your wrist forward. Think of it this way, if you're holding the disc normally, it's going to go up. Your hand and wrist are built that way. You may need to alter your grip a bit to get it level, but thinking about your wrist forward could help a lot. And, just plain throw it lower. Actually, whatever it takes to do that, there's your answer.
Thumb position could help with that, although you'll find that moving your thumb can make altering the flight a bit easier for some types of throw. Don't worry about that for now, concentrate on getting flat, straight flight. Distance will come, worry about consistent straight throws.