From this gif post (taken with permission)

First off, we have

 White carnation: innocence, remembrance

This could both represent the Keneki we see at the beginning of the series, and the inner reminiscing of the past by the current Kaneki.

Don’t forget, don’t forget

Remember who I am

The flower was stained in blood, resulting in a

Striped Carnation: refusal (I’m sorry I can’t be with you, but I wish I could)

This could be viewed as his necessary rejection of his past self, regardless of how strongly he has been clinging on to it so far. This reminds me of these two separate lines in the OP

The me that has stood in this shaken, distorted world-

Was pierced by the memory of the time I laughed so innocently

It starts as just a droplet of doubt, but Kaneki has to accept the reality, no matter how unpleasant it is

and finally,

Red Spider Lily/ Higanbana: the flower of death

Higanbana is a very famous flower in Japan so the meaning is clear here. This flower is associated with loss, longing, abandonment and lost memories. It is believed that if one meets a person one will never see again, this flower will grow along one’s path. I find that there’s are elements of yearning and regret a midst the finality and interpret this as Kaneki being forced to abandon it all- the death to his former self.

I have changed; I can’t return anymore