How to route traffic by proximity from Cloudflare to closest NGINX server?

I'm trying to set up a web server stack in the following way:

• Use Route 53 for my DNS
• Serve static content with Cloudflare from S3 buckets
• Route API calls to nearest NGINX server that sits in front of some Nodejs servers.

So all static content is done easily enough but how can I route my api traffic to the nearest NGINX server depending on location?