Generally "kingdom" can refer to both earthly kingdoms and the kingdom of heaven/God. I think this is the case in Their Eyes Were Watching God as well, and Tea Cake is telling Janie that she is a good person. Also, an illusion is a magic trick. An allusion is when there is a reference to history or culture within a work of literature.
You clearly meant "allusion," so I've made that change in your question.
The first possibility that comes to mind is an allusion to the heavenly kingdom. "The keys to the kingdom" is part of a bible verse; Jesus says that he will give these to Peter (Matthew 16:17-20). This bible passage is common in African American folklore, such as the tale of the "flyin' fool" in The Norton Anthology of African American Literature. It seems to me very likely that Hurston is recording a phrase that she's heard other black people use.
Another possibility, of course, is a reference to Tea Cake's heart. That's not so much an allusion as a metaphor, though. An allusion is a clear reference to something, such a work of literature (the bible counts, of course, as a work of literature). A metaphor is less specific in what it refers to.
In the final line of Chapter 11, Tea Cake tells Janie how much he wants to be with her and expresses his depth of emotion with the words, "You got de keys to de kingdom." This last sentence is a Biblical allusion.
As stated in a previous post, this phrase is used in the Book of Matthew in the New Testament of the Bible. There Christ tells Peter he will give the apostle the keys to the reign of heaven. So for Tea Cake, Janie is all that he could ever desire; she is the ultimate goal of his life. With her love his life will be fulfilled because he will feel as though he is in heaven.
With these words of deep spiritual meaning, Tea Cake engages both Janie's heart and her spirit in equal measure. Janie finds in this man what she has long sought, as he has in her--the opportunity to truly love someone as an equal, and the chance to enjoy life without being a man's mule as with Logan or his simple adornment as with Joe. Together Tea Cake and Janie find happiness, fulfillment as individuals, and the true meaning of what it is like to coexist in love.