It's quite simple to do it using wmic. Try this:
wmic /node:"{computer}" process call create "cmd.exe /c ipconfig /flushdns >> c:\temp\outputflushdns.txt"
If everything is fine you can check something like this in the DOS window where you run it:
Executing (Win32_Process)->Create()
Method execution successful.
Out Parameters:
instance of __PARAMETERS
{
ProcessId = 2692;
ReturnValue = 0;
};
And to check if the command runs successfully check for the existante of the file \\{computer}\c$\temp\outputflushdns.txt (you can manage some scripts to open this output where you run it). Mine shows:
Windows IP Configuration
Successfully flushed the DNS Resolver Cache.