What is spiritual and philosophical meaning of this poem by Rumi?

Flame means to excite. Both worlds are the spiritual and the material. The secret is a past life in Egypt, and he doesn't know if keeping that past life a secret is good or bad.

He's at the highest state of God. He used to have sex with women by looking in their eyes. He is God and is everywhere and so he's not just in one place. He gives spiritual grace, or freedom, but has no name for it.

Shams is Arabic for sun, ie. son, or light, so whatever the son or light of God gave to you in spiritual freedom or enlightenment, the speaker of the poem can also give, because he is just as one with God as God's son.

Rumi feels acutely the suffering of the human condition where we are slaves to our passions and try to fulfill them but always fall short of fulfillment.

His talk of the eyes is not that he was flirting but that he was seeing a world divided into right and wrong, good and bad, and that was a prison for him.

Shams sprung open the door to being, and now Rumi is content just to be a flute in the hands of Shams (an allegory for the spirit that dwells in us)

Now don't put a lot of credence in ideas. Rumi says:

"Out beyond ideas of right and wrong, is a field. Meet me there."

Only there does Rumi really exist not as an idea but as an experience.

Rumi's poems will show you the way.