no dress code I've ever noticed, though my dd went to the Raymond Blanc pop up last year and said it was very smart!. I would start with your shoes, lots of walking, uneven surfaces, gets very wet underfoot in the wet, very crowded so no heels, no open toes. Trainers are your friend.
clothes: floaty, floral and long looks lovely on the preview days but I practice on the public days doesn't work as when you want to bend over to see something you will get dusty or muddy. I usually wear smartish trousers, say linen or chinos with a loose top. take a cardi if it gets chilly . I also have a fold up Mac, (tres elegant not,) that I got at a previous chelsea as a freebie. Don't take an umbrella, though some eye pokers will, the bastards. Proper gardeners don't mind getting a bit damp.
If you have one take a smallish over shoulder bag with a couple of fold ups to put purchases in ,talking of which avoid the tempting stalls on the way in, head straight for the plants, go to the stalls on the way home, otherwise you are carrying stuff all day.
the band area is good for sitting to eat, there are never enough seats in the food areas. Toilets are well organised, you might have to queue for a few minutes but generally well organised by bossy supervisors.
Have a great day, if it is your first time at chelsea you will be amazed. Even after many years I find it hard to believe the show gardens have not been there for years.