NextJS applications run on port 3000 (at least as of the latest NextJS update). I suggest the fly.toml that is autogenerated for Next.JS applications updates its port numbers to reflect this.
That will be done soon: see dockerfile-node/gdf.js at e8cfad57404b473abc9c523725b4ec1a83c1611b · fly-apps/dockerfile-node · GitHub
The plans are to integrate dockerfile-node into flyctl launch in much the same way that dockerfile-rails is.
You are welcome to try it now if you like. The instructions on in the readme. Feel free to create issues, pull requests, or discussions there.