There is no proof that the lyrics were supposed to sound like "blackjack". Donald Fagan and Walter Becker of Steely Dan wrote the lyrics to this song. I have not found any first hand source from them or any other members of Steely Dan that the line was supposed to sound like "blackjack". The general belief is that the lyrics represent a man's failure to learn from his mistakes. Hence, the "Go back Jack do it again" line.
There's a piece written about the lyrics of the song on musicbanter.
Walter Becker and Donald Fagan are well known for writing provocative
lyrics that deal with controversial themes. Due to this reputation,
many fans look deeply into the meaning of Steely Dan's lyrics. While
this works for certain songs, "Do It Again" is not one of those songs.
The general belief is that the lyrics, which touch upon an old time
western scene, infidelity, abuse of trust, and gambling, are merely
metaphoric scenarios used to describe man's complete failure to learn
from past mistakes.
This general ineptitude is examined in each example. Overwhelming
guilt plagues the subject of the first example. He apparently received
a very lucky break with a much-needed second chance. However, he will
most likely fall right into the same trap, making the same type of
mistakes, acting on the same impulses without thinking of the
consequences, and finding himself once again with the deck stacked
The second example used in the song deals with being used by a two
timing woman. Fool me once, shame on you. Fool me twice, shame on me.
The third scenario describes an apparent gambling problem, which
represents the vices, addictions, and compulsive tendencies that
someone is most likely to repeat over and over again, regardless of
the trouble that they bring to themselves and their loved ones.
The third scenario does describe an apparent gambling problem and some may interpret this literally as the table game "blackjack". That really does not appear to be the case. I have heard this song several times and I have never heard "blackjack". I have always heard "back Jack" as the lyrics were intended. However, everyone hears lyrics differently. I still sing the incorrect lyrics even when I know that they are incorrect. It's a force of habit with some songs.