The poem The Heart of the Tree is full of poetic devices. Here is a list of what I have found out so far.

Alliteration
The poet has deployed alliteration in many places to add to the rhythm of the poem. Alliteration is the repetition of consonant sounds at the beginning or stressed syllables of words. Some examples are:

What does he plant who plants a tree?
He plants a friend of sun and sky;
He plants a home to heaven anigh;
In hushed and happy twilight heard —
The treble of heaven’s harmony —

Personification
The poet personifies the tree when he calls it ‘a friend of sun and sky’.

Metaphor
Metaphor is an implied comparison between two different things where there is a point of similarity.

“the flag of breezes free” and “the shaft of beauty towering high” are examples of metaphors in the poem. Here the leafy branches of a tree are compared to a flag and the stem is compared to a beautiful shaft standing high.

Circumlocution
In a circumlocution something is referred to in a roundabout way, using different words rather than stating it directly.

Using “days to be” for “future” and “unborn eyes” for “next generations” are examples of circumlocution in the poem.

Metonymy
Metonymy is a figure of speech where one word or phrase is substituted by another one closely associated with it.

In the first stanza of this poem, there are two metonyms.

He plants a home to heaven anigh; (near the heaven).

Here, ‘heaven’ represents the sky, as we normally think that the heaven is situated somewhere up in the sky. The poet actually means that the man who plants a tree also plants a home for bird high in the sky.

The treble of heaven’s harmony —

Here, ‘treble’ (the pitch range of highest female voice) is used to mean the song or simply the sound which birds make.

The joy that unborn eyes shall see —

‘Eyes’ here means the child, a part of body representing the whole. Thus it can also be classified as a synecdoche, a class of metonymy.

He plants in sap and leaf and wood,

This is another instance of metonymy (and synecdoche) where ‘sap and leaf and wood’ refers to a tree. Parts refer to the whole once again.

Hypallage / Transferred Epithet
Transferred epithet (adjective) is a figure of speech where an adjective grammatically qualifies a noun other than the person or thing it is actually describing.

In hushed and happy twilight heard

Here, the adjective ‘happy’ is used with twilight, though it means people’s happiness in that hour.

Enumeration
Enumeration is the act of listing things one by one. It is “a type of amplification or division in which a subject is further distributed into components or parts”.

In the poem, the poet has conveyed three different benefits of plantation in three different stanzas: maintaining the beauty of nature, duties to future generations and contribution to nation’s growth. The device of enumeration in the poem is detailed here: How has the poet enumerated things In The Heart of The Tree?

Polysyndeton
Polysyndeton is close repetition of conjunctions

He plants in sap and leaf and wood,