If I understand the problem right: You’d need to push that img to Fly registry because Fly can’t deploy from private docker repositories.
Multiple ways to do so: Fly deploy permission denied connecting to Docker daemon - #2 by ignoramous
# (typing these from memory...)
# for machines, I use:
flyctl deploy --local-only --dockerfile <path/to/file> --config <path/to/machines.toml>
# or, build the img and push it to Fly without deploying
flyctl deploy --local-only --build-only --push --dockerfile <path/to/file> -a <app-name>
# create a machine with the img
flyctl m run <registry.fly.io/app-name:img-tag> --schedule=daily --region <r> --name <uniq-name>