Dad looks like a sweetgrass, which is black-winged bronze based with two palm genes..b1b1cgcg. Mom is some kind of blue bird (duh), but there's lots of ways to get blue birds. If she is truly a slate, she is black based with a single dominant blue gene BBDd. She could be a self blue BBDD. It is also possible that she could be bronze based with one or more blue genes bbDD or bbDd. Someone who has raised blue turkeys could probably tell from looking, but I cannot. I suppose she could even be b1b1Dd. The most likely genetic makeup is BBDd. The "not palm" genes are understood in the slate, and the "not blue" genes are understood in the sweetgrass, but a more complete description of the genes in question would be b1b1cgcgdd for dad and BBCgCgDd for mom.
So offspring that get the blue gene from the mom are Bb1CgcgDd. They should look pretty much like blue slates except they carry a recessive palm gene and a recessive black-winged gene. I don't know that either of these genes would show through to produce the barring. Again, someone who plays with blue turkeys might have a better idea.
On the other hand, either parent bird may be carrying additional recessive genes. This is why good notes on breeding are important. So we have a better idea of what genes might be lying underneath the observed colors. If the sweetgrass doesn't come from a sweetgrass line, and is the result of random crossing, there could easily be a Narragansett gene hidden in there.
A calico, by the way, is a Royal Palm with a single red gene. b1b1ngngcgcgRr. They can look a lot like pale sweetgrasses, but I don't think your tom is a calico.
I guess that's really not much help.