Animals do not have a "sixth sense" in the context of having some form of ESP. Many have sensory perception that extends into ranges beyond the limits of human senses, but that just means their sensory organs are more sensitive than ours.

Animals do function on a more instinctive level, whereas most humans like to act on 'reason' or 'logic'. At times, this may give the impression that animals have some supernatural form of perception, but the reality is just that their brains process information on a more primitive level (not necessarily a lesser level) than humans. Further, animals aren't embarrassed by being 'wrong' in their actions, so they won't hesitate to take cautionary action if their brains advise them that a given set of stimuli indicate oncoming danger.

It isn't a matter of having additional senses, only of processing sensory data in a different way and taking resultant action on a more instinctive level.