In the context of the poem where a dolphin speaks of its deplorable condition, it speaks of its feeling. The dolphin constantly feels guilty as it is confined to a pool. Most probably, the man who is there to regulate the dolphins’ movement in the pool as a part of performing tricks to entertain people makes them feel guilty if they do something wrong or can’t perform well. Again, maybe the dolphin feels guilty as it feels it has not been clever enough to escape and have now been caught by humans and kept here in such restricted space.
 
However, the expression ‘a constant flowing guilt’ also suggests the poet’s feeling here. Duffy here upholds herself as an animal-lover and feels guilty that we, the humans are treating animals badly that we shouldn’t do anyway.