Rain Gear, we will ride in the rain. Decent rain gear is essential. You need a Jacket and Pants, ideally they should be Waterproof and Beathable (like GoreTex). A nylon wind breaker is not waterproof. After you finish the merit badge they will be great for troop campouts too!
Water bottle cage, and water bottle.
Small under the seat Bike Bag to carry essentials, OR, Bike Rack and Bag. This lets you easily carry your rain gear, a spare water bottle, and bike tools.
Spare tube! Absolute essential.
Tire levers, Patch kit.
CO2 Inflator, or pump.
All in One Bike Tool
Bike Gloves.
Bike Helmet , required by BSA, it should fit properly.
Maps, check your bike shop for free bicycle maps of Illinois.
Tires, cycling merit badge will be a whole lot easier with road tires. These are smooth and not knobby. They are frequently called City tires or Slicks. You can switch back to the knobbys after you're done with the merit badge.
Floor pump ( to fill your tires at home)
Chain lube (I prefer the dry kind).
You'll want to bring a small tool kit to make repairs or needed adjustments along the way. Tool kits need not be elaborate a simple case with a few tools is all that's needed. You'll need the approriate wrenches and screw drivers to tighten the bolts or whatever on your bike.
This is just a sample tool kit. You will need the tools that are needed for your bike. Remember to think small and light.