to make a judicial investigation
諊 centers on a formal, thorough examination: conducting a judicial investigation to uncover facts.
諊 combines 言 (speech, words) with 匊, which likely contributes the sound. The exact historical development of 匊 is uncertain, but the character is associated with investigation through speech.
Words (言) beside 匊, which looks like a wrapped bundle of rice (勹 around 米). Imagine a judge carefully unwrapping testimony to get to the truth.
For キク, picture a judge saying 'kick' out the false testimony during the investigation: kick -> キク, as the truth is uncovered.