Antiquities of Freemasonry records that the ancient patriarch Jacob "adhered to our science [Masonry] as received by Abraham and practiced by Isaac" and that he passed the secrets of Masonry on to Joseph "whom he lover more tenderly than his other sons" and thus "[h]e bestowed more than ordinary pains in illustrating the objects embraced by the science of Masonry" unto Joseph (Oliver, Antiquities of Freemasonry [1824] p. 196-9, 204). In contrast Jacob's brother Essau was "initiated into and tainted with, the idolatrous rites of the neighboring nations" thus being initiated into a spurious Masonic tradition in which he had instead "taken wives from among the Hittites, and given in other respects to strong symptoms of apostacy". Because of this Jacob was sent to a distant country. It was in these travels that Jacob had his vision of the Ladder.
His mother, to avert the threatened danger [from Esau], sent Jacob to Padanaram, a distant country in the land of Mesopotamia, that he might remain in safety under the protection of his maternal uncle Laban. A fugitive from his own country, alone and friendless, overcome with the bodily exertions of his journey, augmented by anxiety of mind, he laid himself down to rest at a place called Luz, with the cold earth for his bed, and a stone for pillow, and the cloudy canopy of heaven for his covering. Her it pleased the Lord to impart that comfort his situation so imperiously demanded; and which conveyed to his senses through the medium of a most extraordinary vision. He thought he saw a LADDER, composed of staves or rounds innumerable, whose foot was place on the earth, but whose top extended to heaven, and was enclosed with a radiant circle of celestial glory. On this ladder the angels of God appeared as authorized ministers of his dispensations of justice and mercy. Some were ascending to receive divine commissions from the fountain of all goodness, and others were descending to execute these commissions on earth. Suddenly there appeared, amidst the beams of glory which encircled the ladder's top, the Almighty Architect of the universe in person; who addressed the sleeping Jacob in words full of peace and consultation. "I AM the Lord God of Abraham thy father, and the God of Jacob Isaac ... ."
This ladder was a type of Christ, who is the only way by which a created mortal can attain the kingdom of God; for no one can ascend up into heaven, but through him who cam down from heaven. Its staves or rounds point out the innumerable duties man is called on to perform on his journey from this world to better. The most prominent of these, and from which all the rest emanate like rays diverging from a common center, are the three theological virtues, Faith, Hope, and Charity. These virtues are of the greatest estimation amongst Masons, for they form the grand and fundamental basis of their profession.
When Jacob awoke, he consecrated the place, which he conceived to be the house of God and the gate of heaven, by the name of Bethel; he set up a pillar of testimony; and vowed a vow, saying, "If God will be with me, and will keep me in this way that I go, and will give me bread to eat, and raiment to put on, so that I come again to my father's house in peace, then shall I the Lord be my God, and this stone which I have set for pillar shall be God's house; and all that thou shalt give me, I will surely give the tenth unto thee." (Oliver, Antiquities of Freemasonry [1823], p. 198-201)
Thus George Oliver's retelling of the biblical account of Jacob casts him as having been initiated a Mason by Abraham who in turn initiated his son Joseph as a Freemason. In the process of his life Jacob was given a vision of angels as "authorized minsters" descending up and down a Masonic ladder at the top of which was the Grand Architect of the Universe. Next, Jacob, like other Masons, entered into solemn promises at an alter. Afterwards, Jacob would utilize his operative Masonic skills to build a pillar of stone at Bethel and then give it a Masonic dedication as Masonic temple, even a "house of God."
Thus Joseph Smith could have become familiar with the idea of Jacob having being initiated into the mysteries of Freemasonry and begun to envision the encounter at Bethel as a Masonic theophany based solely on his reading of Antiquities of Freemasonry. However, having discussed the role of Jacob's ladder in Masonic thought, let's now turn ourselves back to a discussion of why Joseph may have interpreted the hatched marks on the apron on a depiction from the Book of the Dead Belonging to Nefer-ir-nebu as Jacob's ladder.