Here are two images from my collection that show knit fatigue blouses.
The first shows an unidentified soldier in slouch hat. His knit blouse differs from the vast majority I have observed in photos in that it appears to be sewn together like a typical regulation blouse cut from woven flannel and made without edge binding.
The second image is an unidentified man wearing the most common style of knit blouse with edge binding of woven tape. I have never been able to determine the color of the tape but it ranges from very light to black in other original photos. If I had to venture a guess I would say light blue or tan.
There are many more images of knit blouses (and shirts) that I have collected for my research files that include maybe a dozen more examples being worn in the field for nearly the entire duration of the war. The earliest knit blouses I'm aware of were worn by the 7th New York State Militia as fatigue uniforms. The most common appear to have been gray or "drab" and utilized as Army hospital garments throughout the north. The latest-war examples I've spotted appear in photos taken at Aquia Creek Landing and Petersburg in 1863 and 1864. Beyond the photographic evidence, there is sometimes mention of knit blouses in original accounts or memoirs. Now and then an original quartermaster document will also show them being requested, for example several going to a company in one of the Pennsylvania Reserve regiments prior to the Antietam campaign. One battery of "emergency artillery" raised in Pennsylvania in the summer of 1863 was also issued knit blouses. Since I'm a Berdan's Sharpshooters researcher and collector, imagine my surprise when I saw entries for "knit blouses" being issued in Co. F 1st USSS, these appearing in a company clothing book dating to between Dec. 1862 and August 1863.
A word on how they were likely made. From what I have seen in many other photos the "rib" ran lengthwise much like the warp in woven cloth. The body and sleeves were likely "knitted in the round" (basically a tube, without selvedge) at two different widths. The blouse bodies would have been cut to length, a neckline/gorge cut from the top, the shoulder edges possibly shaped by cutting and then seamed, with armholes cut out of the round-knit material and the sleeves sewn in place. The front would have been slashed open, a one-piece collar sewn into the gorge, and a woven cloth facing hand sewn inside the front to help reinforce the buttonhole stitching and buttons and stabilize the front. All edges at this point would have been raw which is likely why the majority were bound with hand or machine sewn woven tape. The woven tape would also provide stability and decrease the amount of stretch where it was sewn to the knit fabric. Over the years I have developed several sources for the proper 2x2 rib-knit wool for these blouses, as well as two workable patterns and a few prototypes, but had some problems with the knitting mills staying in business. Sadly, the project is dead in the water.