There were therefore seven brethren: and the first took a wife, and died without children.
Note 1 at Lu 20:29: It is very doubtful that the situation the Sadducees were relating ever took place. It is more probable that they were stating a hypothetical case to complicate the understanding of the resurrection and thereby discredit it.
If you accept their basic supposition (marriage continues in heaven), then their reasoning was correct. It would not be possible to administer marriage in heaven with multiple mates, as their story described. Their reasoning wasn't flawed, but rather the "facts" upon which their reasoning was based were not scriptural.
The Scriptures speak of two becoming "one flesh" (Ge 2:24 and Mr 10:8) in marriage, and angels are not flesh (Ps 104:4; Heb 1:7, and 14; see note 2 at Lu 20:36). Paul said, "Flesh and blood cannot inherit the kingdom of God" (1Co 15:50); therefore, marriage is an earthly institution limited to flesh and blood mortals (Lu 24:39) and will not exist in heaven.
Likewise today, many people use very logical reasoning to try to discredit God's Word. But, as Jesus said, they greatly err because the starting points for their arguments are not based on Scripture. Only reasoning based on Scripture have any merit.