Using Rainbow Chard for Spanakopita
Chard isn't as tender as spinach and will require more than just light steaming lest it be chewy and fibrous.

You said you want to keep its bright colors, so I would recommend blanching it in salt water. You need to add quite a bit of salt, such that it tastes like seawater. This keeps plant cells from bursting and releasing pigment. You can rinse your chard after pouring it off to tame saltiness.