I assume that your "chameleon flowers" are the plant Houttuynia cordata. An old friend of mine grew it and when I commented about how beautiful it was she stated emphatically "You DON'T want it!". She insisted that I would be sorry if I planted it in-ground, so I took some and just grew it in a pot for a couple years. It is very pretty and I loved the scent (citrus-like), but unless you want to risk it taking over everything and never being able to rid yourself of it, I wouldn't put it in your garden.

FWIW, there are many plants that will "take over" a garden, or even a yard if allowed to, and people pay good money for them and plant them all the time. I inherited Lily of the Valley and it's just as bad of a monster plant, yet people love it and so do I. I also made the mistake of nursing a little bit of Aegopodium variegata that was inherited with my gardens. Plants like this can be kept in check with barriers and constant maintenance, but with all the gardening I do they just didn't get that constant maintenance and they are both taking over large spaces. sigh.

Thank you for the advice! I think I will pot them...

Many thanks for the advice. This is exactly what i have been looking for.

Here is a link that might be useful: Garden Bags