I don't think you can do this inherently with sqlcmd. What you will most likely have to do is either:

Use your previous method to append results to the same file and then come up with a process to remove the other spaces/headers between your result sets in order to merge them.

or

Output to a separate file and then have a process that parses that file and appends the results to the main output file you want.

There are a few discussions about this already, including one on this site from a few years ago it seems.

SQLCMD append output to file?

https://social.msdn.microsoft.com/Forums/sqlserver/en-US/ea62917d-238f-40ec-bbb4-15217e258191/sqlcmd-append-output-to-file?forum=sqltools

Append output from SQLCMD in batch file

http://www.sqlservercentral.com/Forums/Topic734169-149-1.aspx