Stockinette stitch (all knitted on one side & all purled on the other) will always curl like that, no matter what type of yarn - it's because of the shape of the stitches.
Garter, seed and moss stitches will lie flat. For garter stitch, just knit every row (remember, a purl is just the back side of a knit stitch). Your scarf will be kind of ridged-looking and more stretchy than stockinette.
For seed stitch, alternate knit and purl stitches. Start with an odd number of stitches and knit/purl the same way on both sides - i.e., always start and end with a knit stitch no matter which side you're on.
I don't think I've ever tried moss stitch, but I found these simple instructions:
Start with an even number of stitches.
Rows 1 and 2 - k1, p1 all the way across.
Rows 3 and 4 - p1, k1 all the way across.
Just keep repeating these four rows.
That sounds like it will make kind of a "double" seed stitch, kind of a 2x2 "check" instead of a 1x1.
Knitting the whole scarf ribbed will work too - a ribbed scarf will be narrower and stretchy from side to side.