Museums also have cloakrooms you can leave bags so also worth considering.
Depends on the museum and the size of the bag. British Library won't accept bags over a certain size, otherwise they'd have travellers using Euston, St Pancras and KX using it as a free Left Luggage office.
Most hotels will let you leave your luggage after you've checked out, so if you're in a hotel near to KX, you can just go back and collect on the way to get your train.
As others have said, South Ken Museums are not walkable from KX, but the British Library is nearby - St Pancras station is next door to KX, and the BL is on the other side of St P. There's a free permanent exhibition and usually one or two smaller free ones.
The British Museum is around 15 min walk from KX. But be warned, all the big free museums will be packed. If they are doing bag checks, there might be a long queue.
If DS is into sci fi, fantasy, films, tv shows, etc. (or even if you are!) you and he might like to check out Forbidden Planet in Shaftesbury Avenue for books, comics, merchandise. And the big Foyle's bookshop is nearby.
If using the Tube, plan your journey in advance. (Let DS do it.) So that you know that you need the District and Circle Line Westbound, for example. If you look ahead as you're walking through the station, there will be a sign pointing you in the right direction. The Tube is very well signposted.
Stand on the right on escalators. Nothing marks you out as a visitor more surely than standing on the left on an escalator! Have your card/ticket ready as you approach the barrier.
Wear a cross body bag with valuables securely zipped in an inside pocket, or at the bottom under something else. Don't walk around with your phone in your hand.
London is very safe, but pickpocketing and bag dipping are a risk in crowded tourist areas.
Have a great time!