Most of the time Flex and ActionScript refer to flash platform that enable
developers to create intuitive graphics elements and interactive UI, I plan to
do something that analyzing a huge set of data, and display it with Flex
component.

My initial plan is SOA, but the development process seem to be a bit tedious,
thus i plan to do it all under ActionScript with SQLite locally. My questions
is, is it possible to do so?

Details:
1. It is a data mining algorithm (generating statistics)
2. The input data will more likely be CSV format.
3. Target runtime will be Adobe AIR.

Yes, it's possible.

There are languages that will crunch the numbers and do the I/O faster, but
you usually trade off development time. So, which is more important to you:
speed of development, or speed of program execution? The answer usually comes
down to matters of how much data there is, and how many times it has to run.
If it's gigs of data and it has to run once an hour 24/7, I'd probably build it
in C++.

Put the data mining calculations on the server in some other language, and access results using HTTPService, WebService, RemoteObject, etc.