Several parts combine into one character.

旗 is a phonetic-semantic compound: 㫃 (the "banner-radical" — depicting a flag streaming from a pole) on the left provides the meaning, while 其 (qí, "this / that") on the right provides the sound. The radical 㫃 is one of the more obscure but genealogically rich radicals in Chinese: it anchors a small but conceptually unified family of characters about gathering under a banner: 旅 (lǚ, journey / military expedition — originally a group marching under a flag), 族 (zú, clan / family — an arrow + people gathered under a banner = lineage), 旋 (xuán, revolve), 施 (shī, to give / spread out).

Korean reading "gi." 國旗 (gukgi, national flag), 太極旗 (taegeukgi, "Taegeuk Flag" — the official name of South Korea's flag, with its yin-yang taegeuk symbol surrounded by four trigrams), 軍旗 (gungi, military regimental colors), 校旗 (gyogi, school flag), 旗手 (gisu, standard-bearer / flag-carrier — used in Korean Olympic and ceremonial contexts), 萬國旗 (mangukgi, "ten-thousand-nation flags" = the rows of small national flags strung up at school sports days, an iconic Korean visual).

Mandarin qí, 2nd tone. 国旗 (guóqí, national flag), 五星红旗 (wǔxīng hóngqí, "Five-Star Red Flag" = the People's Republic of China's national flag), 锦旗 (jǐnqí, "brocade flag" = decorative honor banner presented as commendation — a uniquely Chinese institutional gift), 旗子 (qízi, flag — colloquial). And the historically significant 八旗 (Bāqí, "Eight Banners") — the Manchu military and social organization of the Qing dynasty (1636-1912), a system of eight banner divisions that effectively defined Manchu society for nearly 300 years and shaped imperial Chinese governance.

Japanese on-reading キ (ki) — 国旗 (kokki, national flag), 校旗 (kōki, school flag), 軍旗 (gunki, military colors). Kun-reading はた (hata) — 旗 (hata, flag), 旗振り (hatafuri, "flag-waver" = a person rallying others / a leader of a movement). And 日章旗 (Nisshōki, "Sun-Mark Flag") is the formal name of Japan's national flag, distinguishing it from the more widely recognized common name 日の丸 (Hinomaru, "Sun-Circle"). Japanese carefully separates the formal 日章旗 (used in official documents) from the affectionate 日の丸 (used in daily speech).

Memory aid: 㫃 (banner streaming from a pole) + 其 (just the sound) — the streaming flag itself.