Est. 1998 — 27 years of woodworking knowledge
This is not my project but from Reddit. The poster asked how many screws to use, but my question would be are the 2x4's sufficient to support firewood? As for the screw question, their answers ranged from just one on each outside joist to two in each one, so no definitive answer there. Would using more screws provide increased structural integrity?
What say y'all?
Them's 1x4's I think.
I have no other opinions however, and will refrain from my usual sarcasm when it comes to reddit 
@John in NM,
I think you're right, and I see others on the Reddit post have noticed the same. So I guess the question isn't "How many screws?" (the title of the Reddit post) but addressing the framing first.
Moving this to the Beginner's forum because things that may be obvious to y'all are not to those of us who don't know anything about woodworking.
2 placed on diagonal
Well, it looks like the outside rails are let in to the posts, so one screw to keep them there (and some good glue like TB3) would be fine. When doing the same with 2x material and half lap I've used two on a diagonal just because it doesn't hurt and might help a little with cupping.
Not much point in sweating it though, it's not going to last. To do that it will need beefier parts, diagonal bracing, cross supports between posts the short way, etc. And a coat of paint or two for the weather.
When I've had a woodstove, I stacked firewood on disposable sleepers and cross stacked the ends or just ramped the ends. Last house I filled the garage with firewood, since I wasn't parking the car in it. When I was a kid I remember my dad making greenhouse sort of cover for the wood (poplar, it was cheap). The cats loved sleeping in there.
Rural King here sells used RR ties for $20. I think a couple of those and some old pallets would work for me. No tools necessary, it should last a long time, and only $40--plus doctor bills for lifting the ties in and out of my 4x4 F-350. 
I have some plastic brackets that you sick a couple 2x4's in them horizontally and 2 short 2x4's vertically on each end and it has held up well for years. Granted it's only wide enough to hold a rick, not half a cord. Why in the world woud you put floor boards on it?
this is supposed to be for seasoned wood short term or to season wood?
we burned 10 cords per year when I was a kid and split and stacked most of it. Nearly all of our wood was stacked on limbs. About the time I turned 14 or so, oil got cheap and we stopped burning firewood, but in all of those years, we never had anything fall that was stacked just because the limbs were a little irregular.
To the extent that there is a tree available, it also makes a nice center to stack against. several large trees made the turn on our driveway and we used them for that, but a second rank inside of the first around the turn had no such support.
Reddit is a platform that draws attention, and I have of and on participated there, but it's generally a waste of time. To find out it is, all you have to do is torch your ID. People will start to learn that you know what you're talking about. if you give the same advice with a new ID, nobody can tell it's any good. it's pretty much a site for professionals to share a picture of their jobs, and rank beginners who want to refer everyone to paul sellers and james wright or rex whatever his name is. I feel like I conned myself for responding to almost everything I ever responded to there, but I did have a couple of PMs with people who had genuine interest, and back and forth discussion resulted in me being challenged to provide that something would work. it was too infrequent to be worth it, though.
The inability for people to grasp their advice from their own point of view instead of referring you to someone else's video or writings....well, it's like the post above. I guess i conned myself into just responding to the post here, but let people make their mistakes at that level. If you're buying new lumber to store firewood and the new lumber isn't something that will last a long time, it's just weird.