Is there a standard call for flushing the transmit side of a POSIX socket all the way through to the remote end or does this need to be implemented as part of the user level
TCP gives only best-effort delivery, so the act of having all the bytes leave Machine A is asynchronous with their all having been received at Machine B. The TCP/IP protocol stack knows, of course, but I don't know of any way to interrogate the TCP stack to find out if everything sent has been acknowledged.
By far the easiest way to handle the question is at the application level. Open a second TCP socket to act as a back channel and have the remote partner send you an acknowledgement that it has received the info you want. It will cost double but will be completely portable and will save you hours of programming time.