For the benefit of anyone else looking at this question which is quite old
(Apologies to the original author that it did not get answered)
App Insights should now default to using the W3C distributed trace specification (as explained here)
That means that when you enable App Insights against an API in API Management one of two things will happen and either way
(a) A request telemetry is written representing the client request
(b) A dependency telemetry representing the forwarded request to the configured backend
One: If the client request already contains a trace header the trace-Id is used (in App Insights terms this is "operation id"). This is propagated to the backend with a new span
or Two: if the client request does NOT already contain a trace header then a new operation id is assigned and the outgoing request has a new trace header added with the new operation id (or trace-id in w3c terms).