الجواب وبالله التوفيق

It is correct (and proven through Ahadeesof Rasulullah Sallallaho Alyhi Wasallam) to drink Zam-Zam both ways i.e. standing up or sitting down. Additionally Mohammed Bin Abi-Bakr states that he was sitting with Hazrat Ibn-e-Abbas RaziAllah Ta‘ala Anhu and a person came, Hazrat Ibn-e-Abbas RaziAllah Ta‘ala Anhu enquired where the person was coming from. The person responded “from Zam-Zam”. Hazrat Ibn-e-Abbas RaziAllah Ta‘ala Anhu responded saying “you should drink Zam-Zam in the manner it is supposed to be drank.” The person asked, “How should it be drunk?”Hazrat Ibn-e-Abbas RaziAllah Ta‘ala Anhu responded “when you drink Zam-Zam, face towards the Qibla(Khana-e-Ka‘ba), take Allah Subhanahu Wa Ta‘ala’s name and then drink in three breaths, until you are full and then thank Allah Subhanahu Wa Ta‘ala.”

(Sunan-Ibn-e-Maja, 3061)

Hazrat Ibn-e-Abbas RaziAllah Ta‘ala Anhu used to read the following dua while drinking Zam-Zam

اللھم انی اسئلک علما نافعا و رزقا واسعا وشفاء من کل داء (المستدرک علی الصحیحین للحاکم، 1739)

واللہ اعلم بالصواب