A miles ticket could complicate it as normally they can't be combined with a cash ticket.

VS arrives at T3, BA departs from T5 and KLM from T4. There are plenty of landside buses that go between the two as well as a tube / train service. There is a section on the LHR website about terminal transfers.

You would be on your own if the VS flight was late and you missed the next flight.

NOTE that as these would be separate tickets you are not on a connection.

Depending on how late the VS flight is and the reason you could be eligible for compensation under EU261.