The recent Florida school shooting and its causes has been addressed on this site in this question which addresses whether factors other than access to guns are significant based on statements by the Governor of Kentucky suggesting that factors such as the prevalence of violent video games were more important.
The governor made several statements on this topic. In this interview on Youtube he repeats several related claims. But the specific one, not apparently addressed elsewhere here, is this (I hope I'm transcribing his words accurately. The statement starts about 10s into the clip.):
...a hundred years ago and even fifty years ago we had more guns per capita than we do now. It's not a gun problem.
Are his specific claims about the trend in number of guns in the USA correct (specifically that the USA now has a lower level of gun availability than it used to have)?