OK. There’s a fairly long thread on here about the KAW so do a search. There’s also one on bearbones.
KAW thread – https://bearbonesbikepacking.co.uk/phpBB3/viewtopic.php?f=7&t=16216
Our trip: https://bearbonesbikepacking.co.uk/phpBB3/viewtopic.php?f=10&t=20001
My wife and I did it in three days’ riding at the end of May. That was: Sunday afternoon, Monday, Tuesday, Wednesday morning so three bivvies. My riding time was 30hrs. My thought at the time was that was as late in the year as I’d like to do it as many of the singletrack BWs were already nearly overgrown with nettles and brambles. Also a lot of the tracks are rutted and the grass hadn’t grown to hide those ruts – someone I know did it a couple of weeks later and had a rough time.
The KAW is 320km, i.e. 200 miles, assuming you are looking at doing the whole thing that’s 160km per day. Have you ridden anywhere near that with a loaded bike?
If you do plan on doing the whole lot in two days, take as little as possible. As Colin notes: Mat and sleeping bag. Get a summer bag – if the nights are cool it will make you get up in the morning! Inflatable mats take up less space than CCF – Alpkit do one but look up Multimat, the same thing but half the price. If it’s going to rain then a small tarp strung between trees will keep the two of you dry. The official guide talks about wild camping spots being scarce in the eastern part but I don’t remember going much more than a kilometre between possible sites. Further west it’s even easier.
Cooking: it’s only one night and morning. Aim for an evening meal at a pub. For the morning a meths stove (do a youtube search on how to make a soda can stove) and a metal mug will let you make a brew and water for porridge.
Hope for dry weather for the week before – folk talk about things getting bad in the wet and we had really hot weather but there were still some big puddles on the Ridgeway.
Tarp – Alpkit do the Rig3.5, DD hammocks do lightweight tarps as well.
Mat – as above, Alpkit or Multimat
Stove – make your own.
Mug – Alpkit titanium mug – the 400ml is fine but the 650 fits a beer can stove better.
Spare clothing – just something to put on at night when you stop, I take a merino baselayer that’s only used to sleep in – I know it’s going to be dry. Obviously you’ll have waterproofs in case it rains.