Compressing and extracting folders via FileZilla
FileZilla cannot do this. It only allows you to execute FTP command (even with SFTP, which uses SSH).
There are two options:
There is some kind of
WPEngine.com
specific interface that lets you do this.You need some kind of remote desktop or shell access (SSH, VNC, etc.) that allows you to execute custom commands.
If none of the above applies, you cannot rar files.
The wording of your question is not clear, so I am assuming you want the the files transferred to and from your wordpress site to be compressed.
It looks like there is not a standard FTP compression algorithm ("Unfortunately, there is no one standard FTP file compression method; there are HUNDREDS"). You could contact wpengine.com to see if their FTP server supports a compression algorithm, but I would not get my hopes up.
When you use a company like wpengine.com you get the advantage of a syestem which is low cost, easy to use, and easy to maintain, but lose the ability to run custom code. As a result you options are limited to the features and tools they provide. If their FTP server supports compression then you could get a compatable client and use the compression in the site. If you can run custom code on their server then you could get a program which would do the rar compression/extraction for you. Otherwise you will have to upload/download the full size files.
If you need an easy way to transfer files between computers there are many services specifically for this.
As a side note, the FileZilla FTP server does support compression but it looks like you would need the ability to configure the server (which is not possible with most hosts). This can be found in the FileZilla Server Interface under Edit > Filetransfer compresssion.