Direct proof of use
The public record for Kh-59 use in the 2011 Syrian Civil War is caveated. Forecast International's Russian strike-missile profile says the Kh-59MK2 reportedly took part in Syrian combat operations during February 2018, and CSIS Missile Threat reported in May 2018 that Russia may have used the Kh-59MK2 in its Syria air campaign while noting that the claim remained unconfirmed.
The reported Syria use is tied to Russia's brief Su-57 deployment and weapons-testing narrative. TWZ reported that Russian Defense Minister Sergey Shoigu presented video of a Su-57 launching a new cruise missile, said the test occurred in February, and referred to Russian testing of new weapons on the Syrian battlefield; TWZ assessed the missile as appearing to be the Kh-59MK2 but said it was not clear whether that launch took place over Syria.
Sources: Russian Strike Missiles, CSIS New Standoff Missile, TWZ Su-57 Cruise Missile Launch
Timeline
The main dated milestone is February 2018, when the sources place the Su-57 Syria deployment and reported cruise-missile testing window. Forecast International treats the Kh-59MK2 report as Syrian combat-operations participation in that month, while CSIS records the Kh-59MK2 Syria claim as a reported but unconfirmed use.
On May 25, 2018, Russia released or presented video associated with the Su-57 missile launch. CSIS summarized the video on May 30, 2018 as showing a Su-57 launching a Kh-59MK2 air-launched cruise missile.
Sources: Russian Strike Missiles, CSIS New Standoff Missile, TWZ Su-57 Cruise Missile Launch
Narrative
In Syria, the Kh-59 record is best described as reported Russian combat testing rather than a fully confirmed strike history. The available sources identify Russia as the actor, the Syrian theater as the context, the Su-57 as the associated launch aircraft, and the Kh-59MK2 as the reported missile variant.
The sources do not establish a specific target, impact location, battle-damage result, or Syrian-government unit receiving the missile. They support a narrow catalog claim: Kh-59MK2 involvement was reported in Russia's February 2018 Syria combat-test activity, but independent public confirmation of an actual Syrian combat launch remained limited.
Sources: Russian Strike Missiles, CSIS New Standoff Missile, TWZ Su-57 Cruise Missile Launch