It sounds *really* funny to say "I'm a British." The British might say, however, "I'm a British national" or "I'm a British citizen." Likewise, technically you could say "I'm a Chinese" (because technically "Chinese" is also a noun)." But it sounds funny to my ears, so I would recommend just saying "I'm Chinese." However, you can say "I am American" / "I am an American," or "I am Canadian" / "I am a Canadian" with no problem.

Actually, you would very seldom see 'a' used this way, since 'Chinese' and 'British' are adjectives, not nouns. You might see "He is a British doctor." or "He is a Chinese student", but in both cases, the noun ( doctor, student) is required. You might hear people say "I'm a Brit", but that is short slang for British person, so 'Brit' is a noun. You may also see "the British" or "the Chinese", which are understood to be short for the British people, or the Chinese people, respectively.

Both "I'm a Chinese" and "I'm a British" are incorrect. "Chinese" and "British" are the adjective forms of "Chinese" and "British" respectively, so you should always say "I'm Chinese" and "I'm British". You can only use the adjective forms of nationalities as nouns when they end in 'n'. "I'm Australian" and "I'm an Australian" both mean the same thing, except the former uses 'Australian' as an adjective while the latter uses it as a noun. It's the same for "I'm (a) American", "I'm (a) Canadian" etc. The noun form of 'British' is 'Briton', so "I'm a Briton" is correct. To my knowledge, there is no noun form of 'Chinese', so you must always say 'I'm Chinese" or "I'm a Chinese person". There is one exception: people sometimes say "the Chinese" to mean "all Chinese people".

只有中國人會講“I'm a Chinese" ! 因為這個單詞，chinese，它的plural跟singular形式一樣， 因此我們會說“I'm Chinese" （「我是中國來的的」）或者 “I'm a Chinese person" (我是中國人）。因為第一短一點，我們總說哪個。