In the garden, among the rotting magnolia petals and the "rank" ironweed is a patch of purple phlox. Phlox is a genus of flowers that can grow in diverse environments. Phlox means "flame" which is fitting because it can spread. Given this information, phlox is a foil (opposite) to Doodle and the Ibis because it can thrive in a variety of environments whereas Doodle and the Ibis can not.
The empty oriole nest in the elm tree seems eerily similar to Doodle's empty coffin. Recall that when Doodle was born everyone thought he was not going to live. So, they had a carpenter build him a tiny coffin. Perhaps the empty nest symbolizes or foreshadows Doodle's death. Maybe the baby oriole fell. In any case, the empty nest and the empty coffin both suggest the absence of a baby.
The screech owl makes a nest inside the coffin. Brother cruelly takes Doodle to show him the coffin in order to scare him. When he does, the screech owl flies out, scaring them, and in the process they are sprinkled with "Paris green" a poisonous powder used to kill insects. Doodle, named for a bug, is sprinkled with a powder used to kill bugs.
The palmetto might not really be symbolic. The fronds blowing in the breeze do connote a sense of peace. With Doodle safe in the front bedroom, he would be peaceful.
It is significant that Brother names William Armstrong "Doodle" because it refers to a bug. Already, we start to associate Doodle with bugs and animals. He may have similarities to other animals but the labeling of him as a bug also makes him somewhat of an outcast, certainly in his brother's mind.
The most important animal in terms of symbolism is the Scarlet Ibis. The Ibis is native to tropical climates in South America and the Caribbean. Father notes that a storm must have blown it off course. Being an exotic bird, it has had to survive a storm and is not equipped to survive in its new environment. Likewise, Doodle has trouble adapting to his environment, especially with Brother pushing him so much. And the supposition that the Ibis had to endure a storm foreshadows the storm at the end of the story. Note also that when they first spot the Ibis, it is injured. Its wings are "uncoordinated" and it falls to the ground. Doodle is uncoordinated and his inability to live up to Brother's expectations leads to his death.
The bleeding tree's symbolism is straight forward. It is a tree that tends to leak sap, especially when a branch is broken. The color red is significant in this story. The scarlet color of the ibis, the bleeding of the tree, and Doodle's vermilion neck when Brother finds him dead all signify morbid images of blood, wounds, and death.