Abinadi ties up a couple of important images here. He creates a relationship between the atoning Messiah and the people who believe on him. The two images that become relevant are the sewing/seed/growth imagery that is closest to this context. The other is the image of the atoning Messiah as the Father (see Mosiah 15:2-4). Since be begins this particular part of the discourse by insisting upon the Fatherhood, the imagery of the seed becomes symbolically relevant as the metaphorical planting of the seed makes him a "Father."
In the current imagery the distributors of the gospel that allows people to become the "seed" or children of the Father are the prophets. Abinadi has declared that the prophets have declared this atoning Messiah (see Mosiah 13:33-35). They declare this gospel so that the people are prepared for the mortal mission of the Messiah, they become the fallow ground for growing this seed of God. The conclusion they are "heirs of the kingdom of God" depends upon the Father/child relationship that he implies. They are heirs because they are children of their Father, and inheritance is the right of children.