The term in rhetoric for intentionally altering standard English word order of Subject Verb Object (SVO) to another order, for example OVS or VSO or OSV, is hyperbaton. Hyperbaton in its various forms is used to make a memorable point--words "overstep" each other so as to draw attention to ideas embodied in them more dramatically.
Hyperbaton is derived from the Greek word for "overstepping," thus words are said to "overstep." Poets won't employ a method in rhetoric simply to serve the function of making the lines fit the rhyme--or the rhythm; poets choose their rhetorical methods and figures of speech to most impressively make their points and draw their images. Hyperbaton is a figure of speech that depends upon word schemes (word arrangement) rather than word meaning as other figures of speech--such as metaphor and idiom--rely upon.
Your example, "flaunt they in phrases fine," can be analyzed for syntax this way:
flaunt (V) they (S) in phrases fine (O)
Really, it's a little more complicated than this as "flaunt in" comprises a phrasal verb (not in common usage) that is interrupted by the Subject. Nonetheless, "phrases fine" does follow the split phrasal in the Object slot. Yet, the syntax is complicated once again. The normal adjectival phrase oder would be Adjective + Noun whereas Sidney's phrase is Noun + Adjective. Let's see if we can name each variation.
Changing the syntax order from SVO to VSO is an instance of general hyperbaton. A similar example would be "Grow (V) they (S) in courage deep (O)." Inverting the adjective/noun order, as in "phrases fine," from Adjective + Noun to Noun + Adjective is called anastrophe. A similar example of anastrophe is the phrase "courage deep," which in normal syntax would be "deep courage." Again the purpose of hyperbaton, and its various sub-forms is to highlight the idea the words express by making them distinct and memorable.
Sorry for the confusion. I have never heard of syntax alteration and thought that you were looking at "alliteration." Therefore, the question's answer is as follows.
Poets are required to adhere to the rules of grammar as other authors. But poets may also use rhetorical devices to impact meaning and imagery. Spellings can be altered for rhythm, syntax can be altered toemphasize meaning, and pronunciation can be altered for effect. These are all rhetorical devices.
Therefore, many poets change the syntax of a sentence, when examining it in regard to proper grammatical rules, in order to create mood or meaning or imagery.
That being said, what Sidney may be doing, especially in regards to the poem in question, is to representationally compound the fact that love, itself, is confusing by changing the placement of the order of the words.
Alliteration in any poem is used for different reasons by different poets. For the most part, alliteration adds to the lyrical sound heard when the poem is read aloud. (Alliteration is the repetition of a consonant sound in any given line of poetry.)
For example, historically, alliteration is seen in tongue-twisters.
Peter Piper picked a peck of pickled peppers.
Sally sells sea shells down by the sea shore.
Outside of tongue-twisters, many poets use alliteration to add to the quality of the poem. The use of alliteration provides a lyrical sound which adds to the mood of the poem.
Given that you denoted the poem "Astrophil and Stella," (by Sir Phillip Sidney, I am sure that you are looking to examine the use of alliteration in that particular poem.
Since the poem is one which speaks to love, romance, and chivalry, the use of alliteration adds to the mood of the poem. The poem, through the use of alliteration, brings up feelings associated with love and the alliteration makes the poem seem something like a ballad.
An example of alliteration in the poem appears from the beginning.
Loving in truth, and fain in verse my love to show,
That she (Dear she) might tale some pleasure of my pain:
Pleasure might cause her to read, reading might make her know,
Knowledge might pity win, and pity grace obtain;
This was not my question. I don't know why my question has been edited. The original question was:
In general, what is the purpose of syntax alteration in the lines of a poem (other than keeping the rhyme)?
For instance, Philip Sidney says in sonnet 3 : "flaunt they in phrases fine"
The normal syntax will bring the Subject then the verb then the object, or whatever, but in the example he started with the verb then the subject and then the object phrase even when it also needs to be adjusted; it might be like:
They flaunt fine in phrases
So, my question is, what is the purpose of this syntax alteration ( i hope i am calling it the right name)?
thanks in advance.