First off, the medium. There are 3 known mediums for knot-stitch code, each of which has it's own constraints.
Embroidered into fabric
Tapped with fingers on skin
With finger tapping, you're constrained by the number of fingers. This means 5, maybe 4, because while the thumb certainly can be used, it might be used in a different way. For example, if the speaker's hand is on the listener's shoulder, the 4 fingers might be on one side of the shoulder, with the thumb on the other side.
The dot-based nature of knot-stitch code reminds me of Braille, and Morse code. In braille, the dots are arranged in a rectangular grid, while in Morse, they're arranged in a line.
In embroidery, I think it could be done either way.
For knitting, the dots must be arranged in a line. (Or else you'd have to knit half the letters in one line, and the other half of the letters in the next line. I guess this could be done in theory, but it seems ridiculously hard to use.)
For fingers, you could form your fingers into a grid, by putting your first finger under your middle finger, and your pinkie under your ring finger. However, this would be cramped, and awkward, and—when ladies were using it in front of men—would look less natural. So I think line is the way to go.
It doesn't have to be just one or the other. Each letter could have more than one form, the same way written English has both uppercase and lowercase forms, in both printing and cursive. In embroidery—the most common medium—I think grid letters would be easier to recognize, and since embroidery is the most commonly used medium, I'm designing both linear and grid forms.
In written language, people usually write in line. For example, in this explanation, you read to the end of the line, then you go down to the next line, and begin on the other end. However, in a tactile system, I think it would be very hard to find the beginning of the next line like that. So I'm convinced knot-stitch code should be written boustrophedonically.
Because knot-stitch code is tactile, you don't really "see" the letters. Rather you perceive them in the order that you touch them.
If you "read" this line by sliding your finger from left to right, you would perceive the dots in the same order...
...as you would if you read this line by sliding your finger from right to left.
This system involves 3 contrasting stitches. In embroidery, finding 3 different stitches should be easy. In knitting, it could be knit, purl, and... a twisted stitch maybe? (I knit, but I'm a beginner.) In fingers, I imagine it could be (1) fingers simply resting, like on a keyboard or piano, (2) finger pressing with the flat of the fingerpad, and (3) finger pressing vertically, with the fingertip, so the receiver can feel the nail.