What length are the 1x4’s? What are you planning as fencing material? Wire?
There are lots of different ways to build a fence. Some things I’d suggest. Go with something more substantial as corner posts, maybe a 4x4 or 4x6. Brace that back to the next post pretty well. A diagonal 2x4 from near the top of the 4x4 to the ground level of the 2x4 next to it in should work well. If you are using wire, you need that bracing at the corners in both directions so you can stretch it and maintain the tension. The intermediate posts are not that important if you are using wire.
If you are using those 1x4’s, space the posts so that construction is easy. If those are 8’ long, center to center 8’ on the posts works well. If they are 10’ long, then a 10’ center to center post spacing works well.
I suggest you not have a 1x4 or anything else at the top of the fence that chickens might like to perch on unless the run is covered. Chickens like to perch. Most can fly up 6’ without a big problem. If they fly up to perch, who knows what side they might fly down on. And once they are out, they generally don’t know to get back in the same way. Leave a few inches of wire sticking up above your top horizontal brace to stop them from perching.
