If you mean "Can I write Flex apps in C#" or "Can I write
Flex apps in MXML and AS3 using Visual Studio", the answer is no.
But if you write a Flex app, it can access an ASP.NET page using
HTTP, call a web service written in C# using SOAP, etc. In other
words, Flex uses standard internet protocols to access data over a
network; if the server happens to implement those protocols using
C#, Flex doesn't care. However, it cannot directly call remote C#
code the way it can call remote Java code with RemoteObject.
We (my team) went over this 50 times. A lot of the docs talk
about Flex Data Services, which is a java servlett from Adobe that
has a lot of wicked functionality. Like, for instance, they can
propagate changes to other flex apps. There's talk about RPC and
other proprietary protocols. It's easy to get confused.
In the end, Flex doesn't care. We decided to write our own
server in Java and use JSON for the messaging. It just plain works.
So, yes, imho write your server in C#, it will work. Fire up
a debugger in Visual Studio, and another in Flex and watch it