"It is a dirty kitchen."
Translation:Is cistin shalach í.
Why doesn't this sentence need the beginning reference pronoun as with "Is é namhaid phobail é"?
Because it doesn't contain a definite reference. Likewise, your sample sentence shouldn't include the first é.
If you wanted to say "It is the dirty kitchen", you could say:
Is í an chistin (chisteanach) shalach í. In this case, the first í is required for Munster and Connacht Irish, but not for Ulster.