Tube/DLR question- Knightsbridge to West India Quay

Your query puzzled me too, but the solution is that the DLR trains from Bank to Lewisham don’t stop at West India Quay - look at the DLR map on the Transport for London website and you’ll see what it says. It looks as if you can return via West India Quay but have to get there via Canary Wharf station.

However my initial thought was that Bank station is a huge mess, very complicated and I’d always try to avoid it.
You might be better off by taking the Circle or District lines to Tower Hill Station and following the signs at street level to Tower Gateway on the DLR. it means a short walk but you get to see the Tower of London and the flowers etc. on the way

It always comes out as a few minutes more to go via Bank which is why you never see this option. Planners tend to be generally conservative on transfer time but Bank even now is not great for the unfamiliar.

Oddly the fastest way to Bank itself from South Kensington is to take the Circle/District to Cannon Street then walk at ground level.

You might be better off to get to Tower Hill tube station, walk one block to the riverfront to Tower Pier, board the river boat to Canary Wharf, then walk to the Museum of London Docklands.

When you board the boat at Tower Pier, tap in with your Oyster card. Tap out as you exit the boat at Canary Wharf.

Bit pricey at £7.70 each for the one stop boat journey though.