One experiment that can be done at home (because it only tests forest fires on a micro-scale) is an analysis of how forest fires effect the mineral content of soils. Using a soil testing kit (which should include a pH strip to measure acidity), compare the content of normal soil and burnt soil. You will should discover that burnt soil has a higher level of mineral content, which explains part of the reason why forest fires are an essential part of the natural ecological process.
Another experiment you can do at home to understand forest fires can be done completely on your computer. Use the reference below (University of Utah's "The Fire Experiment"), and choose a certain amount of "healthy" trees and a certain amount of "on fire" trees (the initial size of the simulated forest is either 120 by 60 or 600 by 300). "Healthy" trees are green, "on fire" trees are red and trees that are completely "burnt" are black. The simulation will then run based on the numbers that you input and it will give you a sense of how quickly forest fires spread in nature.
Certain plants are grown because they are more drought resistant; this is a process known as xeriscaping. However, there is a threat that these plants are more likely to cause a forest fire. Thus, an experiment could involve taking a group of plants used in xeriscaping and burning the plants; then take a regular group of plants, burn these plants and compare the difference in time. You could vary the experiment by changing the type of material you use to start the fire (e.g., matches in one experiment set and chemicals in another trial run).
Forest fires also pose a great threat to humans, and can cause injuries and loss of life (especially to firefighters), as well as billions of dollars in damage. Thus, many experiments have been done to see how equipment can be improved to fight forest fires. In 2005, the Michigan Department of Natural Resources and Environment started a program called the Roscommon Equipment Center, which has tested several new types of equipment for forest fires, including modifying military vehicles to fire blazes. Some of the equipment that the Roscomm Equipment Center used included mesh gates on tractors; thus one possible experiment you could try at home would be to take smaller models of vehicles and start a small, controlled fire. Then try to add different types of materials (including mesh wiring) which is to see what could make the vehicles most fire resistant.