What does it mean to flow on a beat?
Well In rap, flow is just that, a very smooth, relaxing to listen to 'stream' of lines. A good rap flow gently glides over the rap beat without interfering with how the other instruments in the song are flowing.
What does it mean to rap on beat?
Being on beat means that you're lining up your flow to the tempo and beat of the song. To do this, learn how to count and tap your foot along to music. 99% of western music is based off of 4 beat loops, so all you gotta do is find where the loop begins and follow it counting 1, 2, 3, 4.