It's the leaves, not the flowers, which are used to make a hair dye. They're often combined with rosemary leaves for the purpose.

Simmer 50g of selected herb(s) in 1 litre of water for 20 minutes with the lid on the pan. Cool, strain, and pour the liquid through the hair, catching the rinse in a bowl. Repeat as many times as possible, using the same liquid over and over. Pat hair dry, using an old towel as some of the dye will come off as you dry. The more often you use these dyes, the stronger the colour will be. Commercial herbal teabags can be used, infused in 4 cups of water.

For more intense colour, make a paste by using 1 cup water, 25g selected herb(s) and kaolin powder. Wearing plastic gloves, rub well into the hair and scalp, cover the head with a hot towel and a plastic bag to retain heat, and leave for 20 minutes. Rinse clear.

You might not see an immediate change in colour - the treatment needs to be used regularly, perhaps for several weeks, before you see a difference.

The sage to use for this purpose, and for culinary or medicinal use, is Salvia officinalis. You need to be very careful, because of the hundreds of species of Salvia, only a handful are edible. Best to get it professionally identified.

Here is a link that might be useful: pix of salvia officinalis

Some of the plants in the above link look like veronica to me. Last week I fried a few sage flowerbud clusters and they were delicious. This week they're going in salads.

Here is a link that might be useful: edible sage blossoms