Gathering sp_BlitzFirst data into a centralized database
There's nothing special about the data being built by sp_BlitzFirst. You can really zoom out and ask, "What's the most efficient way of moving data between any SQL Servers?" 

Some of the approaches that folks have used include:


Pulling the data periodically from a central server via linked servers or openquery
Using their favorite ETL tool, like SSIS
Log shipping their management databases to a central location
Writing data movement jobs with PowerShell


There's no one right answer: it's just whatever data movement you're most comfortable with and most able to support. I don't ship a method with the First Responder Kit because frankly, I don't want to do support for this kind of thing. (It would come with all the baggage that comes with anytime people try to connect two SQL Servers to each other, especially over networks.)