These are not flip flops. They are wooden sandals called Geta, slightly elevated off the ground. You can see an example in the image.
They resemble flip flops but are a completely different thing.
Samurai and Japanese people more broadly wore them for the same fundamental reason anyone wears shoes to protect their feet from stones, rough terrain and dirt on the roads. They were made from wood and sometimes rice straw because both materials were abundant throughout Japan.
Japan is also hot and humid for much of the year, which creates conditions that are hard on bare feet over time. The elevated wooden base helped keep the foot away from wet ground and mud.
Another important factor Japanese custom required shoes to be removed before entering a home. Geta were practical for this, keeping dirt and debris outside and preserving the cleanliness of indoor floors. This was especially significant given that many Japanese people slept directly on the floor at night.