The FOIA would be the obvious path to this data. You can get all sorts of government data that way. Often the biggest trouble is knowing that the information exists. If you don't know it exists, you can't ask for it.
and I found the survey question by searching with the filter Question > contains > "firearm."
At this point I'm tempted to say that the author's complaints with respect to data suppression are exaggerated.
Kleck wrote this report once he realized the raw unanalyzed response data (which is what you found) had at some point become available at the CDC site so he could do his own analysis.
>I was able to find this page through Google search
You didn't need to - Kleck's data source is the very first item in the "References" section of OP. It was:
> Centers for Disease Control (CDC). 2018. Behavioral Risk Factor Surveillance System website at https://www.cdc.gov/brfss/annual_data/annual_data.htm. Accessed 2-14-18.