To speak in a regional dialect using animal words in Engpsh, you could use expressions pke:

"The chicken says 'cluck cluck' in my hometown dialect."
"The pigs in my hometown say 'oink oink' in our regional accent."
"The cows in my region moo with a distinct local inflection."
"The goats in my hometown bleat with a particular regional twang."

These are just a few examples, but you could use similar expressions to describe any animal and its particular way of speaking in a regional dialect.