…is not a word. Neither is theirself, or theirselves, nor is it correct if you turn it into two words — their selves — though spell-check will be happy with that.
I suppose there is an apparent consistency to it. Myself and herself seem to be formed out of the possessive, which would make hisself and theirselves seem to make sense, But her, the objective form, not hers, the possessive, is the root of herself, and myself is a vowel shift from meself, which you can still hear in some dialects.
Reflexive pronouns, which is what you call these things, form from the objective — himself, herself, themselves.
But even well educated people, who would never make those errors, misuse reflexive pronouns. “Please give your response forms to Mr. Jones or myself at the end of the presentation.” Wrong. That should be “… to Mr. Jones or me…” This is mostly Mr. Jones’s fault. The speaker wouldn’t have said “to myself” if there hadn’t been someone else in the sentence; they would automatically have said “to me.” Reflexive pronouns should never appear without a pronoun to refer to. “I” has to appear somewhere in the sentence before you can use “myself” — “I did it all by myself.” Similarly “she” needs to be in the sentence before “herself”, “he” before “himself”, and “they” before “themselves.”
Unless you are a Celt referring to your chieftain, in which case Himself (or presumably Herself) becomes a title/name and is treated as such.