Yes, DISTILLING is a Scrabble word!

Letter values in Scrabble US: D 2, I 1, S 1, T 1, I 1, L 1, L 1, I 1, N 1, G 2.

Is it a valid word?

DISTILLING is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

undergo condensation; change from a gaseous to a liquid state and fall in drops
extract by the process of distillation
undergo the process of distillation
give off (a liquid)
remove impurities from, increase the concentration of, and separate through the process of distillation
undergo the process of distillation
extract by the process of distillation
undergo condensation; change from a gaseous to a liquid state and fall in drops
give off (a liquid)

Also: make pure.