The accepted answer isn't really good because it references installing direct RPM as opposed to using repositories which provides better security and easy updates in the future.

The Amazon Linux way is the following.

First, enable the NGINX repository provided by Amazon:

amazon-linux-extras enable nginx1

This enabled a sub-repository with NGINX.

Now, list available versions by running:

yum info nginx --showduplicates

From there, you can decipher that 1.14.2 is not available specifically for Amazon Linux. But that does not mean that you should install random other direct RPM via URL.

Use the closest nearest NGINX version to your requirements, e.g.

yum install nginx-1.16.1

You can install any nginx versions.

Check this: https://centos.pkgs.org/7/nginx-x86_64/nginx-1.14.2-1.el7_4.ngx.x86_64.rpm.html

If you wanna install nginx 1.14.2 follow this:

wget https://nginx.org/packages/centos/7/x86_64/RPMS/nginx-1.14.2-1.el7_4.ngx.x86_64.rpm
sudo rpm -Uvh nginx-1.14.2-1.el7_4.ngx.x86_64.rpm
nginx -v