Is a child's eating a goat's tongue in order for him to be able to speak in accordance with Islamic law, or is it considered polytheism (shirk) with Allah?

Eating birds' tongues is permissible if they are slaughtered according to Islamic law.

As for its effect on improving speech, this should be referred to specialists. If they determine it is beneficial, then there is no harm in consuming it as a remedy. However, if they determine it is not beneficial, then it is not permissible to believe it is beneficial and consume it with that intention, as there is no religious text to support this.