There is a very simple reason why there is no 'kit list' for a sea kayak leader assessment. You should take the stuff you usually take when you are leading groups. However, we all have to start somewhere. This article is a summary of the session I usually include in my sea kayak leader training courses.
You should expect to be equipped to deal with any incident that might reasonably be expected to occur on a sea trip. This is in addition to the things you carry to look after yourself.
First I'll group the equipment into categories, later I'll look at storage and accessibility.
1. Communication equipment.
This will include a VHF radio (either simple or DSC enabled) and some of the following: flares (rocket, handheld red, handheld smoke), phone in waterproof case, LED flare, PLB. You don't need all of these but you do need to have a well thought out selection. Expect to be asked to demonstrate how to make an emergency call whilst on the water.
2. Navigation equipment.
Definitely a map and compass, possibly a deck mounted compass and GPS. It's important that you can read the map. If you need reading glasses for small print, make sure you have though out a way to access them. Consider enlarging map sections.
3. First aid equipment.
You need to have the kit to deal with simple incidents on the water and a more extensive first aid kit for off the water. My immediately available kit is simply a roll of electrical tape; I have a decent first aid kit for use on land.
4. Rescue equipment.
Tow line (deck or waist mounted), knife, pump, contact tow/short tow, tape and clip (dog lead) for joining tow boats in a towed raft.
5. Dealing with broken equipment.
Spare paddle, something to replace a damaged hatch cover (could be a ready made hatch cover - Reed, or plastic and bungee), something to repair a hole in a boat (sylglas, denso tape, flashband), tools to repair broken deck fittings and footrest (probably + and - screwdrivers and allen keys) and a big roll of gaffer tape. An addition to the repair kit could be a couple of large air bags. Instead of repairing a large hole I can fill the hatch with airbag to keep the water out. Of course this won't work if the hole is beneath the seat area.
6. Kit to deal with someone hypothermic.
Available while on land; group shelter, warm layers, sit mat, hot drink, food.
Available on the water; storm cag, warm hat, hot drink, food, pogies.
7. Emergency light
Depending on the time of year and expected daylight hours, you might consider carrying a head torch.
All of this equipment is in addition to the things you carry to look after yourself. You can't give a hypothermic person a hot drink if you drank it at lunch time.
I don't believe that it is the leaders job to carry everything that the group members might need. I don't feel the need to carry spare clothes for people but I do check that they are carrying their own things. Same goes for food.
The next consideration is where to store all this stuff. I tend to group it all into three categories, things that are accessible all the time, things I can access on the water possibly with help, and things I can access only on land.
The easily accessible things include all the navigation equipment, most of the communication equipment, stick-on patches for boat repair and all the rescue equipment. These things are all in my buoyancy aid pockets, on the deck of the boat or in the sweetie hatch on the front deck.
The stuff I can access on the water is in the day hatch. I can open this unaided and it's not the end of the world if it gets full of water. This will include my repair kit, first aid kit, warm hats, food, hot drink, storm cag and pogies.
In the main hatches, which are never opened on the water I store my group shelter, spare warm clothes and insulated sit mat.
This is just the kit that I carry. There are other ways to solve the same problems. What is important is that you can deal with anything the assessor might throw at you. It doesn't have to be a custom made piece of kit, improvised solutions could be just as effective. Get used to carrying all this stuff every time you paddle. You never know when you are going to need it.