sp_blitzfirst results to table on a linked server
There is a note in the script on GitHub:


  Known limitations of this version: 
  
  ...  
  
  
  @OutputServerName is not functional yet.
  


And indeed, that parameter is not used in the proc.  So for now, storing the output to a table across a linked server appears to not be supported.

Since you included the SQL Server 2008 tag in your question, I'll also mention that they don't go out of their way to keep the scripts working on unsupported versions of SQL Server, and you're only a few months away from that end of support date (July 2019!).  I imagine the scripts will continue to work for a while, but there are no guarantees at that point.