In "The Old Chief Mshlanga," how is Doris Lessing celebrating her cultural heritage?

It is not really accurate to say that Lessing is celebrating her own cultural heritage in this story. Lessing was a white British woman born to white British parents, and the cultural heritage celebrated in this story is certainly not that of the white protagonist, who comes to learn that the racist attitudes of her parents are unfair and reprehensible. However, we can certainly say that Lessing is drawing upon her own experiences of having been raised in Africa. Through the eyes of her white protagonist, Lessing criticizes the point of view which leads to cultural oppression, while signposting the true value of the African culture which the white colonizers dismissed.
Elements of Lessing's own culture, such as the snatch of Tennyson's "The Lady of Shalott" the protagonist sings, are set against the backdrop of "the warm soil of Africa," which the white child "might be supposed to accept . . . as her own." But Lessing's narrative is highly critical of this cultural appropriation: because the child knows only of "the names of little creatures that lived in English streams," she imagines these things in the African landscape, even though they do not belong there. She has been taught to impose her own taught culture upon her lived experience, so that "it was the veld that seemed unreal" and the black people among whom she lives are a "faceless" and "amorphous" "black mass." The child, indeed, has been explicitly taught to take them for granted and that she should not even attempt to understand them. Her mother even berates her for attempting to talk to any of the black servants, saying that they should not talk "to natives." A distinction has been drawn between the child and those she is in daily contact with, and the bent of the narrative reinforces the fact that the children of the colonizers were taught to paint their own British culture over the native culture even in their imaginations.
The child's perspective changes only when she encounters a different kind of group, natives who "had an air of dignity, of quietly following their own purpose." The shift in perspective here is marked by a shift in the narrative, from third person to first person. Through the person of the chief, Lessing shows the dignity of the black natives which she had not previously understood, to the extent that being polite to them is "difficult, from lack of use." At this point, the narrator begins to reconsider what she has been taught, particularly after reading that the place in which they live is "Chief Mshlanga's country." After this change in perspective, the narrator says, "that other landscape in my mind faded, and my feet struck directly on the African soil."
Having properly come into contact with African people, the narrator is able to see Africa for what it really is, seeing "the shapes of tree and hill clearly." At this juncture, she still feels that "this is my heritage too; I was bred here . . . there is plenty of room for all of us." But this is a naive interpretation, as the narrator learns after she has made a pilgrimage to find the chief in his own village. She finds the village "indifferent," and it instils in her a sense of a "queer hostility in the landscape." The narrator, despite her hopes of living alongside the natives, still at heart wishes she could "call [the] country to heel like a dog." This underlines the colonial arrogance still inherent in any idea that the land could, or should, be "shared" between the invaders and the invaded, who had no choice in the matter.
At the end of the story, Chief Mshlanga speaks, through the narrator's cook, saying "all this land, this land you call yours, is his land, and belongs to our people." And yet, soon enough, the village ("kraal") is moved because it "had no right to be there," and Chief Mshlanga's people are moved two hundred miles east, to a "proper Native Reserve," evicted from the land they had lived on for centuries. The "lush warm valley" would be appointed to another white man, who also would believe it was "his heritage, too," and his lot. But the tone of Lessing's story, as it comes to a close, leaves us in no doubt that it is not the heritage of the white settlers which deserves to be celebrated and which has been unjustly destroyed.