If you're asking about serial number records, such as sales records on specific rifles. They are few and far between. I have one in my collection. I've come across 3 of them (including mine), all from the same shipment to the same club. I looked at the SRS volume 4 and counted them out. It was less than 75. This is largely because how the paperwork was processed.
A rifle club had to apply to be in good standing and recognized by the NRA, the NRA Secretary would write a letter certifying the club was in good standing and eligible to purchase from the program. The Chief of Ordnance would authorize the sale through the State Adjutant's Office who would order the rifles through one of the arsenals around the country. Each Arsenal was responsible for a few territories or states (which seem to be determined by proximity to the arsenal). The arsenal would ship the rifle, ammunition, targets, infantry equipment (whatever they wished to purchase). Based on how the sale was processed, it seems the Chief of Ordnance only got receipts of eligibility to purchase. The actual sales receipts and shipping tickets were processed at the arsenal or armory level.
It gets more detailed from there, but that's the basic design of the program and why the Chief of Ordnance in Washington DC didn't get many invoices to ship rifles by serial number. The Chief of Ordnance files are where Mallory got a lot of his files and serial numbers for his databases and newsletters.
Now If you're talking about records about the program, there's a mountain of paperwork that I've been digitizing from both DC and College Park. I was at the regional archives location at Philadelphia this past July, there wasn't anything substantial at that location concerning sales to rifle clubs.
I'll be at the Boston Regional Archives in March of next year, there "may" be something there. But time will only tell.