This is not the correct way to think about it.

To receive the benefits of Skyteam status, you must be travelling on a Skyteam-coded flight (i.e. a flightnumber starting with DL-, KL-, AF-, AZ-, UX-, etc; NOT a flightnumber starting with VS or any other non-Skyteam member airline) AND that flight must also operated by a Skyteam-member airline (i.e. the flight is operated by Delta, Air France, KLM, Alitalia, or any other Skyteam member).

This is not the case when you are travelling on a Virgin Atlantic operated service - VS is not a member of any alliance. They therefore do not observe Skyteam status (or oneworld status or Star Alliance status, for that matter!!!)

The exception is if a particular Skyteam airline has a partnership with the particular non-Skyteam airline in question, and in that case, it only applies to members of that particular Skyteam airline's FFP. For example, Delta and Virgin Atlantic have a deep partnership that involves more than codesharing (Delta owns 49% of Virgin Atlantic shares), so the two airlines extend reciprocal frequent flyer benefits to members of each other's programmes. As such, Delta Skymiles members have their status perks observed by Virgin Atlantic. This is due to a bilateral agreement in place between the airlines, and has nothing whatsoever to do with Skyteam.

For now, AF and KL only have a codesharing partnership with Virgin Atlantic - therefore, a Flying Blue status member will not receive any status perks when travelling on a Virgin Atlantic operated, or Virgin Atlantic coded, flight. Flying Blue members will receive miles and XPs for KL or AF coded flights operated by VS, though.

But watch out! If you somehow ended up on a VS-coded flight operated by either AF or KL, you would receive no XPs or miles in Flying Blue.