According the Tennessee Conservative (citing numbers from 24/7 Wall St.), gun sales are down from their historic highs, but people are still buying a lot of firearms. Below are the rankings and rates in the four states served by this website. Also included in first place (per capita) is Kentucky. The #1 state by total volume is Illinois at 6,707,482.00.
Keep in mind these numbers are based on background checks. Background checks are useful but not definitive because some checks involve more than one firearm, some checks are declined or the sale canceled, and the checks do not capture private sales between unlicensed individuals – except where private sales are prohibited.
Illinois has 3.38x the rate of checks as Kentucky despite having a much lower per capita rate. This is likely a reflection of Illinois law vs. the laws of other states and may help us glean some insight into just how many gun sales are not captured by background check numbers. I seriously doubt that Illinois citizens purchased 5.6x more guns than Texas citizens or 6.33x more than Floridians. The primary difference seems to be that all sales of firearms in Illinois require a background check.