Q.Why our Madrone seems to have died
Although the Madrone is a slow growth tree, it was doing well for the 5 years since we had it planted. Then after a lot of rain in January, it started turning brown and the whole tree was brown and dried up. What could we have done to prevent this?

It does sound as if the Madrone Tree died of root rot following heavy rain.
My research shows some other disease issues with Madrone Trees.
Here are some articles and links that may help you determine an exact cause and possible remedies should you choose to plant again.
https://www.gardeningknowhow.com/ornamental/trees/madrone/madrone-tree-information.htm
https://catalog.extension.oregonstate.edu/sites/catalog.extension.oregonstate.edu/files/project/pdf/ec1619.pdf
http://calfire.ca.gov/foreststeward/pdf/treenote16.pdf
http://online.sfsu.edu/bholzman/courses/Fall02%20projects/Bioegeography%20of%20Pacific%20Madrone.htm