Liza, I start with natural or white fabric for dyeing. I think indigo will overdye a chemical dye but no others that I know of.
I do sometimes use soy
milk as a binder on cellulose fibers to give a natural dye some protein to adhere to.
Raven has a thread devoted to woad
https://permies.com/t/76750/fiber-arts/Woad-growing-harvesting-dyeing
Here's one on indigo
https://permies.com/t/37159/fiber-arts/Indigo-blue-growing-harvesting-processing
The links at my pictures above are to a more general dye discussion.
I tend to add dye plants to the mix everywhere as many of them are also attractive to pollinator's and many quite beautiful.
Bright
Lights cosmos, for example, give that wonderful deep orange from the flowers and the butterflies and hummingbirds love them. I pick the blooms to dry just past full so everyone has a chance. They keep blooming all summer because of the deadheading and there's always lots of seed for next year and volunteers.
Beware, as you might have already found out, there's a 'rabbit hole' of information out there
"We're all just walking each other home." -Ram Dass
"Be a lamp, or a lifeboat, or a ladder."-Rumi
"It's all one song!" -Neil Young