Which one is the appropriate sentence? 

......have you been knowing her? 

The phrase "have + been + verb-ing" forms the present perfect continuous tense. This tense is used to describe actions which started in the past, continued for a period of time (for a duration) and is still ongoing now. It will likely continue into the future. 

......have you known her? 

The phrase "have + verb (in past participle form)" forms the present perfect tense. This tense is used to describe actions which started in the past and the effect of the action is still present now. The focus is on the starting point (in the past) and the present moment.   

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The phrase "how long" already imparts the meaning of duration. Hence, we are just trying to find out the moment we got to know her, since it's understood that we definitely still know her now. Therefore, we use present perfect tense to form this question. 

Hope this helps.

Cheers, Lance