Yellow Belly from my understanding is as follows:-

The soldiers from Lincolnshire wore Blue and white tunics.
They were stuck in a field, fighting for many days and trapped by the opposition.
Nobody had taught these soldiers about always peeing downwind.
Instead they peed straight into the wind and after many days of battle, were seen to be running away.
The white had turned to yellow due to the wee splattering back onto the white parts of their tunics, which happened to cover their bellies.
Somebody seeing them fleeing said "here come the yellow bellies".

Since then all people from Lincolnshire have learnt to pee downwind from a very early age.