yes ... absolutely. Flex works great with ColdFusion. You can use remoteObject calls on the Flex side to call functions inside your cfc. Your cfc function must be set to access="remote" . The remoteObject endpoint points to your coldfusion server (e.g. http://www.yourdomain.com/flex2gateway/).
This is a good place to start
Yes I know I can do all that when coldfusion is installed on my hard drive, but in this case
I can ONLY access the CFC over the internet.
I don't have LAN access. I can't mount a drive or browse to select the CFC
You are saying its still possible to develop against the flash remote cfc's when
you do not have access except via http?
Yes. No need for local CF server or LAN.
All you need http access to your remote CF Server via the endpoint url in your remoteObject call http://www.yourdomain.com/flex2gateway/
When debugging or running Flex web or air app locally, you can still get data from your remote CF server.
<s:method name="getPhotos" result="getPhotos_Result(event)" />
Hope this helps.