Refers to the lead ship in a fleet, commanded by a flag officer. Also used metaphorically for the most important or leading product, store, or entity in a group.
その空母は艦隊の旗艦だった。
The aircraft carrier was the flagship of the fleet.
この
This new smartphone became the company's flagship model.
This store is our company's flagship store.
This battleship serves as the fleet's flagship.
機関 is a completely different word meaning 'organization' or 'engine' that happens to share the same pronunciation きかん with 旗艦, so listeners must rely on context to tell them apart.
期間 means 'a period of time' and is another common homophone of 旗艦, distinguished only by context since both are pronounced きかん.
flagship store; flagship shop
Compound of 旗 (ki, 'flag') and 艦 (kan, 'warship'), literally 'flag warship'. The term originated from the practice of a commander flying a flag on the lead ship.