A single flow'r he sent me, since we met. (1)
The poem's first line can be read in two ways: either as a statement of fact (the speaker has only received one first), or as a complaint (as in, he's ONLY sent me one rose, and should have sent me more). Later, we will find out that this girl doesn't want any more flowers.
All tenderly his messenger he chose; (2)
The speaker's guy seems like a nice, lovey-dovey guy. He is capable of tenderness after all. His tenderness, however, just isn't enough for the speaker, as she lets us know later.
'My fragile leaves,' it said, 'his heart enclose.' (6)
These lines tell us that the flower symbolizes the man's heart. However, if we take them more literally, it's almost like the guy doesn't have a heart (because it's in the flower). Of course, it also seems that the sender of this heart-flower thing is, by association, a fragile fella himself. This makes the speaker's rebuke of his gift all the more pained.