Vknitter, that scarf looks woven but you could get a similar look with knit. The back side will not look as perfect as the front side like it would in the woven scarf, but would not be bad looking. The finer the yarn you used the smaller the stripes would be (lots more knitting as well).
For the horizontal stripe you would just knit one row with the black and then pick up the yellow again. I would work on double pointed needles, either two long (long enough to comfortably hold all the stitches you plan to use) straight ones or use a circular needle of any length. Knit the number of rows you want of the yellow always planning for it to end up at the right hand side (where you are ready to begin a right side row) when you want to add in the black. Then from the right side work 1 row of black, then don’t turn to purl back, but slide the stitches back to the other end of the needle so that you are again at the beginning of a right side row. The yellow would be there waiting for you and you would pick it up and knit a right side row again. That way you could carry the yellow all the way up the side and only have to cut the black and work it in at each use. (be sure to work the black ends into the black stripe)
For the vertical stripes I think I would do it the way the vertical stripes are worked on this sweater pattern LINK Scroll down to where the pattern explains the stripes: it says “vertical stripes”. These are done with a crochet hook after the scarf is knitted. If you have any experience with a crochet hook (or can find a way to learn) this is not hard to do and pretty much looks knit on. (duplicate stitch is another possibility, but I think the crochet is faster and easier)
The other option would be to do one stitch intarsia work. I have never done this (but I have done intarsia), but it might be possible to just work the one yellow strand all the time and carry it across the back for the stripe. (try a little swatch and see how it works) Look up how to do intarsia. I believe there is information on this site in the “view videos” section on the bar at the top of the page. Run your cursor over that and a drop down menu will appear. Choose “advanced techniques”. On the page scroll down and look for it.
I haven’t seen a pattern for a scarf like this, but it would not be hard to make one yourself. It sounds like you have enough knitting experience to do it. Plan out how many stitches you would need and where exactly the black stripes will fall row wise. Perhaps use some graph paper to keep track of things. Then write out your plan in a way you can follow it.
The other thing to keep in mind is that a woven scarf lies nice and flat, a scarf knit all in stockinette would curl badly on the sides and ends as well, so you would need to put some sort of flat stitch on the ends and sides to prevent that. Seed stitch might be a good choice. But stockinette in the middle would work best with the vertical stripes (at least the crocheted stripe, or duplicate stitch, the intarsia too I think).
Those are some ideas and things to think about any way. Have fun with your scarf.