Which "english" is proper?

When someone says to speak 'proper english', are they referring to 'the Queen's' english or the American dialect.?

To speak 'proper english' means that you are using correct grammar, not dialect. So, quickly both forms of english could be proper if grammatically correct.

You'll NEVER speak 'good english' but you may always speak english well.

English is a relatively young language. It is highly expressive and most importantly it is always evolving. Words enter the language through usage. French for example is controlled by an academy of scholars who determine what is a proper word. Can you say 'stagnate'. As far as proper English, well that debate is ongoing. Generally speaking a 'proper' speaker does not use slang or profanity.

As others have said, English is evolving. One already sited example is good and well. Technically 'good' is an adjective and 'well' is an adverb. It is correct to say something is 'good English.' but you would say that someone 'writes well.' This distinction is fading as using 'good' as an adverb as well as an adjective is slowly being accepted. Saying someone 'writes good' is incorrect from a strict grammar point of view but in a few years or decades it will probably be accepted.

This battle has already been lost with the word 'fast.' At one time 'fast' was properly an adjective but years of it being commonly used as an adverb made it acceptable in both places, otherwise we would have to use 'rapidly' or 'quickly' in its place. I'm not sure why we don't just say 'fastly' and 'goodly' to be consistant since that is the standard way of inflecting an adjective into an adverb..

Of couse what is proper English will always depend on the context. Computer people have a habit turing turning verbs into nouns (e.g. the startup, the backup, the upgrade) and nouns into verbs (Let's database that, provision those servers). Most treat the plural data as singular saying 'the data is....' instead of 'the data are...' Among computer people these things are all proper.

Some authors use poetic license to intentionally break the rules of grammar for effect.