I know next to nothing about Nix at Fly except there's a few folks who are looking at it at Fly. The repo at https://github.com/fly-apps/nix-base shows how its working for a Rails app. Is that enough to get you running with Nix flakes?

Beyond that https://community.fly.io is the best place to get help with Nix on Fly since my abilities are exceeded. There's a Rust thread at https://community.fly.io/t/running-reproducible-rust-a-fly-a... that touches on nix flakes.