In Russian colors are:

Красный, оранжевый, жёлтый, зелёный, голубой, синий, фиолетовый.

I mnemonic:

Каждый Охотник Желает Знать Где Сидит Фазан.

Which can be translated as: Every Hunter Wants to Know Where the Pheasant Is Sitting.

Dunno any mnemonics, but the colors in Portuguese in the order listed are vermelho, laranja, amarelo, verde, azul, (unsure about indigo) and violeta / roxo.

Never heard of such a mnemonic in German, nor the concept of a rainbow consisting of 7 specific colors. A rainbow contains all colors, so it's pretty arbitrary which of them you list.

Obviously, we do teach kindergarteners to draw rainbows, but you usually just use all color pencils you have. You probably don't have an indigo pencil, or it would be called "dark blue" or "lilac" here.