Hello,
Here's what I found in an older aviculture book from my collection: FINCHES The diet of finches is best if it remains very simple in order to be certain that it will be consistently followed. Basically, it consists of finch mix, health grit, greens, a dietary supplement, an insectile mix and cuttlebone. Some birds require some modifications such as the addition of extra niger, extra canary seed, fruit, mealworms, and spray millet. Some of the larger finches can use Parrakeet mix instead of finch mix.
Finch mix consists of four parts Australian millet, two parts plain canary, one part white proso millet, and one-half part oat groats. No red millet is used. Most pet shops carry a good finch mix. Some include niger and other seeds in their mixture, but the writers prefer to feed this ration in a separate dish.
"The writers"mentioned are Henry Bates and Robert Busenbark, the book is "Finches and soft-billed birds", published by T.F.H.Publications, Inc., Jersey City 2, N.J. in 1963. No idea about "proso millet"!
I know, it's not exactly the term finch seed. Because somehow it sounded rather familiar (that is, in Dutch: vinkenzaad), I checked the Dutch term, which turns out to be the name of a small wild plant: Neslia paniculata (older name: Vogelia paniculata). In English it is called Ball Mustard of Common Ball Mustard, it it found in Europe and Asia and belongs in the family Brassicaceae (cabbage, mustard, etc.). It has small yellow flowers. Nothing is said of any use as bird feed; I suppose it can be given to birds, as the seeds are the normal globular type like mustard and cabbage seeds, but you might know that canaries, for example, are not fond of those. In Dutch we have an old expression "op zwart zaad zitten"= to be left with black seeds, for: being short of means (like a canary which has only cabbage seeds left to eat, edible as they may be) . . .
Cheers, good luck, enjoy the birds and their health.
Jan van der Brugge, Netherlands