from which public buildings is this flag flown?
From the flag pole above the front entrance of 10 Downing Stree.
Flag of the United Kingdom

Two days later, Prime Minister Gordon Brown announced that with immediate effect the Union Flag would fly from the flag pole above the front entrance of 10 Downing Street on every day of the year. 
who fought in the battle of goodenough island? Allies and Japanese troops from the "Kaigun Rikusentai". when did the battle take place? 22–27 October 1942. who won? The Allies. what strategy did they use to win? UNANSWERABLE which countries were part of the allies? France, Poland and the United Kingdom. what is the weather like in the first country? Hot-summer mediterranean climate and the warm-summer mediterranean climate. please name some of the cities you can find here Paris, Lyon and Marseille. what language is spoken in the second country? Polish. what is the capital? Warsaw. what sports are played here? Volleyball and Association football. is either of these sports played by the third country? Association football. what religion do they follow in the thrid country? Christianity. does this country use symbols for any purpose? Yea, The flag of the United Kingdom and Britannia. can you please describe the flag The national flag of the United Kingdom is the Union Jack, also known as the Union Flag. where did it originate from? UNANSWERABLE in what scenario would you fly the flag at half-mast? The Union Flag can be flown by any individual or organisation in Great Britain on any day of their choice.
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Flag of the United Kingdom [SEP] Flying from public buildings
Two days later, Prime Minister Gordon Brown announced that with immediate effect the Union Flag would fly from the flag pole above the front entrance of 10 Downing Street on every day of the year. The intention was to increase feelings of British national identity. Other Government departments were asked to follow this lead, and all Government buildings in Whitehall did so.