So confused!

Emma and Mr. Knightly are not brother and sister but they are related to each other by marriage since Emma's older sister Isabella is married to Mr. Knightly's younger brother John. They are actually in-laws and the comment "we are not so much as brother and sister to make it improper" is simply a joke more in part of Emma since she is young and playful and she likes to tease Mr. Knightly sometimes. Apart from being an in-law, my Knightly is also a close friend of the Woodhouses and is always welcomed at Hartfield. I hope that answers you question.

In addition to what Greenwoodelf said, it was quite common then to refer to one's brother-in-law as simply brother or sister-in-law as sister (in Pride and Prejudice, Lady Catherine uses brother to refer to the relationship between two unrelated men who marry into the same family, saying that Darcy and Wickham would become brothers by marrying the Bennet sisters). Using the same terms for one's spouse's family as for one's own family reflected the idea that marriage was not just between the couple, but marriage joined together the two families of the couple; which is why Emma and Knightley refer to each other as brother and sister, although they are not technically related.

There will come a time when you believe everything is finished. That will be the beginning.

mr. (george) knightly's brother, john knightly, is married to emma's sister, isabella.
they are kind of brother and sister-in-law.

I doubt you would understand.

Also, Emma is referring to a custom that brother and sister did not dance together. (But because they are in-laws, not actually related to each other, it is not improper.)