Since the announcement of the partnership both airlines have been working to integrate their systems. You can book Virgin Atlantic now with Delta Skymiles without fuel surcharges.
Virgin Atlantic has a fantastic business class product that is almost as good as first class on many other airlines.
While not great – Virgin Atlantic has ok business class availability for the members of Flying Club.
Delta.com shows Virgin Atlantic (if available) just fine if you enter it segment by segment.
However that's were the good news ends. Delta does NOT have access to the same award inventory. It's just a very small subset. 90% of the seats are not available to Skymiles members when using miles.
Here's what I suggest you should do:
1) In recent calls I got VERY helpful Delta agents who were willing to look up inventory for the whole month per segment. That's the fastest way to do it (or subscribe to Awardnexus). Determine your route (and alternatives) and let the agent search the whole month. The US East Coast seems to have more availability than the West Coast but some SFO flights are available.
Virgin Atlantic's route map is rather easy at this point, so there are only so many options.
2) Note down the available VS flights.
3) Build other flights around it (positioning flights, onward flights) using delta.com or expertflyer.com if needed.
4) Compile your valid itinerary and read it to a Delta agent and try to get it booked that way.
– Delta Skymiles does not allow routings to Asia via Europe
– you can route to Africa via Europe – potentially giving you 4 legs on Virgin if you find availability
– Delta.com' award calendar works only on delta flights so you have to use it day-by-day – it's better to call and let the agents do the work for you