The problem lies with 2 elements: the security group settings & the ftp server settings.
FTP is not considered a good solution for passing files between EC2 instances and your computer as it is not firewall "friendly" - you can't just open port 21/TCP on the amazon security group settings because the server is actually sitting on a NAT address and when an ftp client connects to an FTP server using PASV mode then the server tells the client which port and which address to use for the data stream (like directory listing).
If you want an alternate easy solution for transferring files between yourself and the EC2 instance then setup a dropbox on both machines - it doesn't get easier than this... :)
If you still want to set up an FTP server on your EC2 instance then read on...
Typically, people just try to open port 21 and then try to connect and get something similar to:
Status: Server sent passive reply with unroutable address. Using server address instead.
Response: 425 Can't open data connection.
The solution is (and for this example I will explain how to perform the setting on FileZilla FTP server on windows):
1. FileZilla FTP server: Edit-> settings -> Passive mode settings:
(x) Retrieve external IP from:
[ this tells the ftp server to perform a 'whatismyip' and give that to the ftp client, you can also specifically put the address DNS name you use in your remote desktop in the "Use the following IP:", e.g., ec2-6-100-129-60.compute-1.amazonaws.com ]
(x) Use custom port range:
[ these are the ports that will be given to the ftp client - we will open them in the following step in the Firewall ]
2. Amazon security groups: open ports -
a. Custom TCP rule , Port range:21
b. Custom TCP rule, Port range:1024-1048
3. Turn off the windows firewall on the EC2 machine (you don't need it - you have the amazon firewall)
That's it, and just as side note, you don't need to use Elastic IP feature for this to work.
Also don't forget to set your client to use PASV mode (which is typically the default).
You can verify this works by reading the answer the server gives the client when it enters PASV mode:
Response: 227 Entering Passive Mode (174,149,71,102,4,7)
This response means: "Yo FTP client, use 188.8.131.52 and port 4*256+7=1031"