As a general rule, most people say 1,000 rounds per gun but I don't think that's very intelligent. It's more than enough for a short term event such as a riot or hurricane but totally inadequate for a long term event. If you're anticipating combat, bear in mind that our troops in VietNam frequently carried 600 to 1,000 rounds while on three day patrols instead of the allotted 200. And they sometimes used all of it!
So here's what I'm thinking. It depends of what kind of rainy day you're anticipating. Are you thinking of a riot situation such as S. California a few years ago or the chaos following Hurricane Katrina or are you thinking of an total end of world scenario aka The Living Dead or are you anticipating a total ban on new ammo? If you're thinking of a riot then a few hundreds rounds should be sufficient. If you're thinking of a ban then obviously you'd want as much as you can afford and can store. If you're thinking of an end of world then most people would say all you can get. But here's something else to think about; I think that they forget that it's likely they'd have to move to a safer, more defensible location. If they do have to move then how to they plan on moving say 5,000 rounds of .308 ammo??? If I was worried about this last scenario I would STRONGLY consider at a small lightweight caliber instead a more powerful caliber such as .22lr or .22 Hornet instead of .308. You may not be able to kill everything on this continent with it but you can carry a thousand rounds of .22 in a couple of large pockets, you can't hardly carry a thousand rounds of .308!
Personally I don't worry about an end of world scenario but the others do concern me somewhat. I don't try to hoard huge amounts of ammo but I do buy mine in large quantities (case size lots, MOL 1,000 rounds) every time that I need ammo so I do have a good amount on hand and it also has two other immediate advantages. One, is that it's cheaper. Two, is that since all the rounds are from the same lot, they shoot consistantly and I don't have to re-adjust my sights until I buy more ammo, usually not for many years. As it turns out I haven't bought hardly any ammo since well before the current rush on ammo and buying a large amount back when it was cheaper has turned out to be a dam smart thing to do! Everything that I own has lost value except the ammo!
PS I keep reloading tools, lead and bullet moulds and plenty of powder and primers for all of my primary weapons. If something does happen, I will also be able to reload ammo as a secondary reserve. Given time I could easily load well over 30,000 rounds with what I have on hand right now. And like the ammo, all of this stuff has gone up in value significantly in the last few years so they're a good investment even if I never had to use them.