The kindle and charger are fine in your hand luggage, I think you're not supposed to put a kindle in checked luggage because ofbthe battery. You 0will have to put the kindle, but not the charger, in a tray, unless you're lucky and get one of the scanners where you can leave everthing in your bags - there will be signs.
My top tip is not to try to put everything into one tray, use two or three so that your phone, kindle, bag and coat aren't all squashed into one but are in single layers- a mistake i make a lot! Don't worry if your bag is pulled for inspection - you may have left something in it, eg bottle of perfume, or it could be a random search. Happens to me a lot, but causes just about a 5 minute delay usually.
I've always left eye liners in my bag, putting lipsticks, mascara and liquids into my plastic bag. Remember that you can buy toiletries at the airport past security or get them in a supermarket wherever you're staying, but they will need to meet the liquid limits if you intend to bring them back as hand luggage.
If you're in a hotel or BandB - and even lots of AirBandBs too - there will be shampoo, soap and probably conditioner, so you won't have to bring your own.
My top tips are 1 don't wear any make up so you can test expensive face creams in the duty free, and 2, bring an empty water bottle so you can fill it up from the water fountains past security, I just can't bring myself to pay £3 for a bottle of water.
Have a fantastic trip - travel is complicated and confusing, so