Themselves is correct and a reflexive pronoun in English. Theirselves is incorrect and not used in English.
They need to call the police themselves.
Themselves is the reflexive pronoun for the pronoun “they”. We use a pronoun in place of a noun when we don’t want to state the noun. A reflexive pronoun is when the pronoun is both the subject and the object of the sentence. This happens for example when the person(or people in this case) is both the doer and receiver of an action.
They had to cut the grass themselves. They had no gardener.
Theirselves is incorrect and should not be used in English.
“Theirselves” is used in some parts of the English-speaking world instead of “themselves”.
“Their self” is not used as a reflexive pronoun but can be used in another context. “Self” is a noun that means a person’s essential being. In this case, you can use “their self”
Their self has many layers.