How is language being used in a figurative manner in the poem "They Flee from Me" by Sir Thomas Wyatt?

The most obvious metaphor that governs the poem "They Flee from Me" by Thomas Wyatt is the comparison of women (or lovers) to animals, and perhaps more specifically to deer.  In this unrequited love poem, the speaker--obviously a male--describes how women who formerly slept with him willingly now run away from him, much like deer who venture close to a human bearing food and later flee.  Here taking bread becomes a euphemism for sex.  Words such as "gentle," "tame," "meek", "wild," "range," apply both to women and to deer.  
The first stanza speaks of women (or deer) in the plural, but the second clarifies  the fact that this poem is really about one specific lover.  Here we have sultry imagery describing the woman who initiates the relationship with the speaker.  

When her loose gown from her shoulders did fall,
And she caught in her arms long and small . . .

She asks the speaker "Dear heart, how like you this?" The words "dear" and  "heart" are particularly effective here because they serve as puns.  "Dear" and "heart" are homophones for "deer" and "hart," respectively.  These puns reinforce the deer metaphor and tie the woman's seduction of the speaker to the first stanza by giving a specific example of how he was "stalk[ed]." Somewhat ironically, it is the woman who is the aggressor, the stalker, while the man is her willing victim.
In the last stanza, specific word choices indicate the woman's rejection of the speaker and his resulting bitterness.  His "gentleness" is now unappreciated.  She has moved on to "newfangledness," quite possibly suggesting new lovers. The word "kindly" is ironic in referring to how he feels she has treated him, and the speaker closes with wondering what she now deserves.