If I play Kennen from my champion unit zone, will it trigger the ability of Kennen legend ability?

Yes. Playing a Kennen champion unit from your Champion Zone triggers Heart of the Tempest's ability.

The Legend reads: "When you play a card from anywhere other than your hand, empower me." By default, you can only play cards from your hand or your Chosen Champion zone (Rule 419.1.a). The Champion Zone is not your hand, so playing a card from there squarely meets the trigger condition — the Legend will empower.