Grading: (1) This hadith is sahih, and this isnad is "hasan" because of Muhammad bin Amr - who is Ibn Alqamah al-Laythi - and he has been corroborated.

Reference / Source: It was also recorded by al-Bazzar in his "Musnad" (3455) via Abd al-A'la bin Abd al-A'la, from Muhammad bin Amr, with this same isnad, at length, in the wording: "A drinker was brought to the Prophet (peace and blessings be upon him) and he ordered that he be beaten, so they beat him with whatever was in their hands (sandals, sticks and the like). Then when it was the time of Abu Bakr (may Allah be pleased with him), a drinker was brought to him and he asked about his beating (its amount), so we estimated the beating we used to give the drinker in the time of the Messenger of Allah (peace and blessings be upon him), and we reckoned it at forty (lashes). So Abu Bakr (may Allah be pleased with him) gave him forty lashes, and then (later) Umar (may Allah be pleased with him) gave eighty (80) lashes."

Reference / Source: It was also recorded by al-Tirmidhi in "al-'Ilal al-Kabir" (416) via Yahya bin Sa'id al-Umawi, by al-Nasa'i (5265) via Azhar bin Sa'd, by al-Nasa'i (5267) via Mu'tamir bin Sulayman, by al-Baghawi in "Mu'jam al-Sahabah" (1889), al-Tahawi in "Sharh Ma'ani al-Athar" 3/ 156 and al-Daraqutni (3324) via Muhammad bin Bishr al-Abdi, and by al-Baghawi (1889) via Abu Usamah Hammad bin Usamah. All four of these narrators narrate it from Muhammad bin Amr with this same isnad.
Technical note / Defect ('illah): In his second narration al-Nasa'i joined "Muhammad bin Ibrahim al-Taymi" with Abu Salamah, and likewise did al-Baghawi, al-Tahawi and al-Daraqutni, who also added "al-Zuhri" along with him.

Technical note / Defect ('illah): Al-Tirmidhi said: I asked Muhammad (i.e. al-Bukhari) about this hadith, and he said: "They have differed over this hadith, and I do not consider the hadith of Abd al-Rahman bin Azhar to be 'mahfuz' (preserved)."
Important point: We say: it has another route which will come shortly in the author (al-Hakim)'s work as number (8329), via al-Zuhri from Abd al-Rahman bin Azhar at length, in which it is mentioned that Abd al-Rahman bin Azhar witnessed the incident at the Battle of Hunayn.
Details of the narration: And al-Bazzar said: "We only mentioned the hadith of Abu Salamah and Yahya bin Abd al-Rahman bin Hatib from Abd al-Rahman bin Azhar because the two of them did not narrate any hadith from Abd al-Rahman bin Azhar other than this one, and we do not know of any isnad narrated for Abd al-Rahman bin Azhar with better connection than this isnad, even though al-Zuhri did meet him."

Reference / Source: It was also recorded by al-Nasa'i (5266) via Muhammad bin Abd Allah al-Ansari, from Muhammad bin Amr, from Muhammad bin Ibrahim al-Taymi, from Abd al-Rahman bin Azhar, in the same way.

Reference / Source: It was also recorded by al-Tahawi 3/ 156 via Nafi' bin Yazid al-Kala'i and Anas bin Iyad, from Yazid bin Abd Allah bin al-Had, from Muhammad bin Ibrahim bin al-Harith al-Taymi, from Abu Salamah, from Abu Hurayrah (may Allah be pleased with him).