Direct proof of use
The Mk 15 Phalanx was documented in the 1990 Gulf War during a February 25, 1991 ship-to-ship friendly-fire incident involving USS Jarrett and USS Missouri. A U.S. Department of Defense GulfLINK account says the warships were shelling Iraqi-occupied Faylakah Island with HMS Gloucester when an Iraqi shore launcher fired a Silkworm anti-ship missile, Gloucester destroyed the incoming missile with a Sea Dart, and Jarrett's Phalanx CIWS, operating in automatic engagement mode, fired at Missouri's chaff.
The same account says an estimated four 20 mm rounds from Jarrett's Phalanx struck Missouri's superstructure area, with one round penetrating thin upper metal and no casualties reported. This makes the documented Gulf War use a shipboard close-in defense engagement event, but not a successful Phalanx intercept of the Iraqi missile.
Sources: GulfLINK Friendly-Fire Incidents
Timeline
On February 25, 1991, USS Missouri was conducting Gulf War fire-support and deception operations off Kuwait. The Battleship Missouri Memorial describes the battleship feinting an amphibious assault and says HMS Gloucester fired Sea Dart missiles when a Silkworm appeared to be headed toward Missouri.
GulfLINK's incident summary places Jarrett two to three miles off Missouri's port side during the engagement. Missouri launched chaff as a countermeasure; Jarrett's Phalanx then fired a short burst at the chaff, and several rounds hit Missouri after their energy was largely spent.
Sources: Battleship Missouri Gulf War History, GulfLINK Friendly-Fire Incidents
Operational role
In Gulf War service, the documented operator was the U.S. Navy aboard USS Jarrett. The relevant role was shipboard air and missile point defense for coalition naval forces operating off Kuwait, although the recorded firing resulted from an automatic engagement against countermeasure chaff rather than a missile kill.
The Navy describes the Mk 15 Phalanx as a fast-reaction, radar-guided 20 mm gun system that gives ships an inner-layer defense against anti-ship missiles, aircraft, and littoral threats. GulfLINK's older Navy fact file similarly describes Phalanx as a terminal defense against anti-ship missiles that have penetrated other fleet defenses. In the February 1991 event, that intended terminal-defense role was present in the engagement context, while the actual missile defeat came from HMS Gloucester's Sea Dart system.
Sources: U.S. Navy Mk 15 Fact File, GulfLINK Navy Phalanx Fact File, GulfLINK Friendly-Fire Incidents