Driving it'd be about two miles and take maybe ten minutes in average busy-ish-but-not-too-busy traffic. TFL estimates suggest that a black cab would cost somewhere between £8.60 and £13.80. A minicab would be cheaper, but they'd have to get one.
You could make sure your DD has the Hail-O app downloaded on her phone (assuming she has a smartphone) and you have an account all set up and authorised (you could link a credit card if you're feeling brave), then she could get a black cab from that if you're concerned about her hailing one.
It's not too far to walk, but it'd take them more like half an hour, I think. It's not a bad idea so long as they have a map -- alternatives would be walking to Sloane Square (more practical from the coach station than Victoria itself) and getting the tube to South Ken (but that would only save them about ten minutes, which they could easily waste buying tickets) or getting the C1 bus (which would only save about five minutes).
OH dear my route failed to copy but it was a fairly standard one off my iPad, zig zagging up, only hitting the A40 just before they reach the NHM. It would take about 35 mins though as BikeRunSki said.
It's not far, but it's more than 15 mins! More than 30-40. Tbh, it is a very simple tube journey from Victoria. They want to get the District/Circle Line 2 stops West through Sloane Square and get off at South Kensington. SK is a small station and there is a well signed, well used, well lit tunnel from tge station to the museums. The whole journey will take about 15 min.
It is walkable - I often walk it. But it will take about half an hour and is actually quite a tricky one to navigate. I say that as a Londoner who walks everywhere. I don't normally say it but on this occasion I would get the tube or the 360 bus from outside the coach station.
DD, aged 16, is going to London with her boyfriend on a day trip, as they want to go to the NHM. They are both bright kids, but can be geographically challenged! Having looked at maps, they have worked out that they can walk from Victoria Coach Station to the museum, and it should take about 15 minutes. I don't know this area at all, but a friend has said that it's too far to walk.
Is it too far for two healthy 16 year olds? If so, is there a bus they can take? I'm not sure I trust them to get there on the tube, as neither of them have ever been on it.
They will have phones, so will be able to look at a map or satnav if needed, but I'd like them to print out a map too and know where they are going in advance.