I don't have any intrinsic problem with the police asking for information. It's not unknown for crime labs to canvass stores to match fibers from some particular lot of carpet or clothing, then ask for sales information for those items.
The NRA link simply links to the Orlando Sentinel site, which contains this line in the article:
"The problem is that Florida law prohibits law enforcement or any other government agency from requesting and compiling the personal information of gun buyers."
If true and properly represented, it would appear the Daytona PD is itself committing a criminal act. My understanding of the Alice-In-Wonderland of criminal law is no better than that of any other layman, but as I understand things, any evidence derived from the information they receive would be tainted and inadmissible, as would any other evidence derived from that information. I believe the crude phrase is "fruit of the poisoned tree."