My lazy way is NGINX with autoindex.

If it's to go over untrusted network (e.g.: internet, school network) I use SSH for port forwarding. Lazy encryption.

Something like this works just fine:

worker_processes 1;
daemon off;
events {
}
http {
        default_type application/octet-stream;
        server {
                root /storage/emulated/0/sharedfile;
                listen 127.0.0.1:30000;
                location / {
                      autoindex on;
                }
        }

}

sharedfile is a directory with the files.
On remote machine if I am not mistaken

ssh -L 127.0.0.1:8080:127.0.0.1:30000 username@host

Then just access it in web browser on 127.0.0.1:8080 or whatever port you chose.
In PuTTY you can find this under "Tunnels".

Of course, you need to have SSH server set up as well.