2-color k/p flexible long-tail cast on allows you to cast on using two colors. There is no need for a long tail, because you will be using two different balls! Just make a slip knot of the two yarns and put it on the top needle, then pick up the two yarns as you would for the long-tail, keeping track of which color is which!
Working 2-color k/p flexible long-tail cast on
For this application, do not count the slip knot as a stitch. Make your slip knot of both C1 and C2. Set up for the flexible long-tail cast on below having C1 over your forefinger and C2 over your thumb. The loop on the top needle will be the opposite color from the loop on the bottom needle.
*Work a loop onto both the top and bottom needle as described below. [There will be a loop on the bottom needle and a loop and the slip knot on the top needle. This will create a knit stitch in C1 on the top needle (and a loop of C2 on the bottom)].
To create a C2 loop on the top needle: Bring the needles, held together, to the right of the yarn on your forefinger. Bring the needles underneath and upward into the loop on your forefinger. Twist the needles over and grab the right-most C2 thumb yarn onto the top needle, and bring the yarn and both needles out of the C1 loop on the forefinger. Before removing your finger to tighten the yarn, put the C1 loop onto the lower needle, remove your finger, and tighten the yarns.
Repeat from * for the correct number of stitches. When working the next row or round, do not work the slip knot. Drop it from the working needles.
This 2-color k/p flexible long-tail cast on technique can also be done with 2 strands of a single color.