The flower in question is a Forget-me-not.
One theory is that the poem of the same name, by McGonagall1, is the story upon which AnoHana is loosely based2.
McGonagall's Gem, Abridged
In the poem, a knight falls into a river after foolishly leaping over a river to fetch his betrothed a flower which she asked for, then realizing he couldn't swim (...while swimming back), finally crying "Forget me not", while handing her the flower.
It would seem Jinta plays the role of the Maiden, and Menma the role of the Knight.
The other theory is that Menma is coming back to remind Jinta et al that she's still there; many of them have become withdrawn, and want to forget about her death.
Poppo actually puts various flowers into the jar at Menma's death site, Daisies being among them. Something tells me he's not in on the whole Forget-me-not voodoo.
And finally yes, the Blue Bookmark is also a Forget-me-not.
1: He is arguably one of the worst poets in British history, which makes me ponder why such a gem was chosen for a noitaminA show.
2: There is no official word of this, but McGonagall's story seems in-line with the circumstances of Menma's death; they're both based on the forget-me-not, and they're both accidental drowning while their loved one watched.