For those unfamiliar with Roman Jakobson, the correct quote is (with italics from the source)
The poetic function projects the principle of equivalence from the axis of selection into the axis of combination.
The quote comes from Jakobson's influential closing statement "Linguistics and poetics" at the conference on "Style in Language" held at Indiana University in 1958. It was revised and published in the conference proceedings Style in Language, edited by Thomas Sebeok, in 1960. The noun "hallmark" does not occur in Jakobson's text.
At the beginning of his talk, Jakobson identifies six basic functions of verbal communication, including the referential, the metalingual and the poetic function.
The poetic function is not limited to poetry; it is also used, for example, in "advertising jingles" and versified scientific treatises. But only in poetry does it have a "coercing, determining role" (Jakobson).
To turn to the question more specifically, there is no such thing as an "equivalence to the axis of combination". The type of equivalence that Jakobson sees at work on the paradigmatic axis is based on sound, metre and rhythm. He describes "equivalence" as follows:
In poetry one syllable is equalized with any other syllable of the same sequence; word stress is assumed to equal word stress, an unstress equals unstress; prosodic long is matched with long, and short with short; word boundary equals word boundary, no boundary equals no boundary; syntactic pause equals syntactic pause, no pause equals no pause. Syllables are converted into units of measure, and so are morae or stresses.
So Jakobson does not mean that the semantically based selection that works on the paradigmatic axis (roughly an equivalence in meaning) now also functions on the syntagmatic axis. The equivalence on the syntagmatic axis is based on sound; examples of equivalence in sound include rhyme and metrical patterns. Caesar's famous quote "Veni, vidi, vici" is an example: three disyllabic words (one type of equivalence based on syllable counts), each stressed on the first syllable and beginning with the same consonant (alliteration) and ending with the same vowel (a rhyme).
With this in mind, the word "rose" in "a rose is a rose is a rose" is an example of sound-based equivalent, but of an easy sort, because the word is simply repeated. "A rose is a rose, I s'pose" would also achieve equivalence on the paradigmatic axis. The verb "s'pose" is not part of the same word class as "rose", nor is it semantically related, so it is not even on the same paradigmatic axis as "rose". In that sense, it is not of an "equivalent type" as "rose". I don't think C. S. Peirce's distinction between types and tokens, if that was an intentional reference by the question, is helpful here.