All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
The prominent scholar Mubaarak-Poori wrote a chapter in his wonderful book The Biography of Imaam Al-Bukhaari which he entitled: Chapter about the marriage of Al-Bukhaari: Did he get married? Did he beget any children?
He quoted some statements of Waliy Ad-Deen At-Tabreezi, the author of Mishkaat Al-Masaabeeh as well as statements of Mulla Al-Qaari, who elaborated on Mishkaat al-Masaabeeh, saying that Imaam Al-Bukhaari did not leave any children. They quoted statements of the prominent scholar Al-'Ajlooni, who doubted the marriage of Imaam Al-Bukhaari and said that if he got married, we would have found mention of this in written texts.
Mubaarak-Poori favored the view that Imaam Al-Bukhaari got married, giving evidence of the story that was mentioned by many scholars, among whom was Ath-Thahabi in Taareekh Al-Islam and Siyar A'laam An-Nubalaa’, that Imaam Al-Bukhaari gave money to his writer as a consolation and told him, “I have female slaves and a wife, and you are single.” This is a text which proves that Al-Bukhaari had a wife and that he had female slaves.
As regards whether or not he had children, then it was reported – as you mentioned – that goods were sent to Al-Bukhaari from his son Ahmad. Ath-Thahabi mentioned this report as well. But other sources mentioned that the goods were sent to him by “Abu Hafs” instead of “his son Ahmad”; this was cited by Al-Khateeb in his Taareekh and by Al-Haafith in At-Taghleeq and in the introduction of Al-Fat-h. This is what Mubaarak-Poori stated, then he mentioned the statement of Al-Haakim that: Al-Bukhaari and Muslim did not have children.
Therefore, there is no clear evidence, as you see, whether or not Imaam Al-Bukhaari got married and whether or not he had descendants; Allah knows best about the reality. In any case, this is not an important issue that leads to doing deeds; it is enough for us to know that Imaam Al-Bukhaari wrote a chapter in his Saheeh which he entitled: Encouraging marriage, for the saying of Allah (which means): {…then marry those that please you of [other] women.} [Quran 4:3]; then he mentioned the hadeeth by Anas, who related that the Prophet said, “...and I also marry women. So the one who does not follow my tradition in religion, he is not from me (not one of my followers).”
It is believed that he followed this Sunnah (and got married), as seen in his story with the writer. As regards having children, then this matter was not in his hands, as is known; Allah says about himself (what means): {...He creates what he wills. He gives to whom He wills female [children], and He gives to whom He wills males. Or He makes them [both] males and females, and He renders whom He wills barren. Indeed, He is Knowing and Competent.} [Quran 42: 49-50]
Allah knows best.