KiCAD symbol editor - how to use insert key to duplicate pins with every other number
I'd place all the pins in order, alternating left and right, leave the orientation as it is, and then finally go over to the right side, hover above the pin and press r twice to rotate it. You can also combine that with placing the pin, by hovering above it, pressing m to start moving, and pressing r twice while moving.

Selecting multiple pins and rotating them at once also works, but will reverse their order as it also rotates their coordinates around the center of the selection.