DCMS say in a statement:
It is with great regret that we learn of the death of the King Abdullah bin Abdulaziz, King of Saudi Arabia.
It is requested that all flags be half-masted from 8am today until 8pm this evening.
Any other UK national flags flown alongside the Union Flag when it is at half-mast should also be at half-mast. If a flag of a foreign nation is normally flown on the same stand as the Union Flag, it should be removed.
Flying flags at half mast on gov buildings for the death of Saudi king is a steaming pile of nonsense. That is all.
— Ruth Davidson (@RuthDavidsonMSP) January 23, 2015