One of the “problems” with the flat brioche stitch is that the stitches between
the knit columns on the RS are worked in a garter stitch and require more height
than the knit columns. This forces the garter stitch column to zig-zag in order to
fit into its place. That’s why you get the uneven looking stitches.
The other problem is that this stitch wants to bias.

Use either circular or double-pointed needles to avoid having to cut threads.

To begin, loosely cast on (long tail over 2 needles) an even number of sts with
color A. My colors: color A = deep pink, color B = light lavender

Row 1 WS color B: *k1, yf sl1yo, rep van *. Do not turn work.
Row 2 WS color A: Slide to other end of needle to pick up color A, *p1, brp1;
rep from *. Turn work.
Row 3 RS color B: yf, *sl1yof, p1; rep van *. Do not turn work.
Row 4 RS color A: Slide to other end of needle to pick up color A, *brk1, k1;
rep from *. Turn work.
Rep Rows 1 through 4.

To begin, loosely cast on (long tail over 2 needles) an even number of sts with
color A, foll row is color B, foll row is color C, rep this color sequence. To start a
new yarn, tie it in a knot to the yarn hanging, you can untie it when finishing and
weave it in.
My colors: color A = old rose, color B = yellow green, color C = dark blue green

Follow these instructions using the A, B, C color sequence.
Row 1 WS: *k1, yf sl1yo, rep from *.
Row 2 RS: *brk1, k1, rep from *.
Rep Rows 1 through 2.