The rest of this post contains spoilers.
The film opens with Jones as a teenager. He tries to reclaim the Cross of Coronado from treasure hunters but fails, and it's given over to the character listed as "Panama Hat" in the credits. One of the significant things about him is that he's wearing a red flower (I don't know flowers, so I can't be more specific):
Additionally, the framing here - especially the rack focus from Young Indy and the sheriff to Panama Hat as he steps into view - ensures that attention is drawn to him (and to a lesser degree his flower).
Along with explaining facets of Indy's character (including his hat and whip), this whole sequence differentiates between those who seek artifacts for wealth and personal gain (like Panama Hat) and those who don't (like Indy, who insists that the Cross of Coronado "belongs in a museum"). I think to some degree, the flower that Panama Hat is wearing indicates this selfishness throughout the movie. Or at the very least, flowers indicate characters who you shouldn't be so quick to trust.
Only a few minutes later, Walter Donovan is introduced, and he's wearing a red flower - just like Panama Hat:
Donovan's flower indicates both of these aspects - Donovan is seeking the Grail for himself (unlike Indy, who seeks the Grail for the sake of his father - first finding and then saving him), and he's not a character to be trusted. Later he says, "Didn't I warn you not to trust anybody, Dr. Jones," including himself in the "anybody."
After Indy and Brody get to Venice, they meet Dr. Elsa Schneider. While walking to the library where she and Dr. Jones (that is, Indy's father) were researching, Indy himself steals a flower to give to her:
Elsa's actual interest in pursuing the Grail is harder to determine than either Donovan's or Indy's. At times, it seems like she's after it for herself (like when she's trying to reach it after it's crossed the seal and the floor is breaking apart), but at other times, she seems more interested just in the endeavor to find it (like when they're looking through the tombs to find the second marker).
Regardless, she's also not a character to be trusted when she's first introduced. Indy does and later finds that she's in league with the Nazis.
And finally, there's Kazim from the Brotherhood of the Cruciform Sword:
He's almost the opposite of both Elsa and Donovan because at first it appears that he's a bad guy (knocking out Brody and chasing Indy and Elsa through the tombs and the canals), but he actually turns out to help Indy by telling him where his father is and later distracting the Nazis as they're travelling to the Canyon of the Crescent Moon.
He's also opposite them because he's not seeking the Grail for himself. In fact, he's not even seeking the Grail; he's trying to protect it. After Panama Hat sets the standard, the characters in the movie who are wearing flowers generally turn out to be self-seeking and untrustworthy, except for Kazim.
