One picture holds the whole word: a thing with flames coming off it, burning where everyone can see. Hold that picture and the other uses fall out of it. Leaves can be so red that the tree looks like it is burning. A person can be so that something inside seems to burn. The fire is real in the first use and borrowed in the others, but the look is the same every time: hot, bright, impossible to miss.
Aflame comes from Middle English a-flame: the old prefix a- meaning 'on / in the state of' plus flame (from Old French flame, Latin flamma). The literal sense is 'in flames', which is exactly the picture the modern word still carries, and it explains why aflame behaves like asleep and awake in a sentence.
aflame 來自中古英語的 a-flame。a- 是一個老的字首，意思接近「處在⋯⋯的狀態」；flame 是火焰，經古法文 flame 來自拉丁文 flamma。字面就是「在火焰之中」，跟今天的核心畫面完全對得上，也說明了它為什麼跟 asleep、awake 一樣習慣放在 be 動詞後面。
Wiktionary etymology supplied in this evidence packet (kaikki:3f6f69a190036ae4:506261444:11227): Middle English a-flame < a- + flame/flaume/flawme < Anglo-Norman flaume < Old French flame < Latin flamma.
Two branches
真的著火
這一家就是核心畫面本身，沒有比喻。
adjective · C1
Burning, with flames coming out of it, so that you can see the fire on the thing itself; it is usually used about something large or whole that has caught fire, such as a building, a field or a hillside.
著火的／整個燒起來
像火一樣的顏色與情緒
這兩個意思都不是真的著火，而是把「正在燒」那個樣子借過來形容別的東西。共同點是強度：又紅又亮，或又熱又激動，一眼就看得出來。兩個都習慣接 with，把「燒的原因」講出來。
adjective · C1
Glowing with strong warm colour or light, so that something looks as if it is burning; it is very often followed by with and the thing that gives the colour, as in trees aflame with autumn leaves.
火紅發亮／豔得像在燒