If one depends entirely on a reading of 1954's LIVE AND LET DIE, the only answer one can surmise is that he didn't particularly care about the sociopolitical struggles for the cause of "Negro emanicipation" (as Mister Big calls it). Yet even that observation is qualified by the fact that LIVE is intended primarily as an escapist thriller. Such a work, as I've argued in my other two Fleming essays, is not defined by its realistic political content.
When 007 first arrives in America to seek out contacts for his mission, he reflects upon the fact that all the American authorities will know him, so that he must sacrifice his spy's anonymity, making Bond feel "like a Negro whose shadow has been stolen by the witch-doctor." This reflection foregrounds Fleming's need to convince his readers that the majority of black people are inherently superstitious, the better to make Mister Big's voodoo empire seem somewhat probable. Given the amount of research Fleming did on contemporaneous American culture, I think it very unlikely that he seriously believed that most American blacks were regular practitioners of voodoo rituals, or even conversant with the basic concepts of the Haitian religion. It's more believable that Fleming simply posited this misinformation as a "one gimme," by which he could unify Mister Big's spy network through a religious ideology.
Further, black characters are not the only ones who believe in voodoo. The Caucasian Solitaire believes in her own psychic talents, and though the novel doesn't provide irrefutable proof of their reality, once or twice she does seem on target. Even Bond, though not a believer, does not scoff at the immense persuasiveness of the religion-- and more, he does so without the usual recriminations. Voodoo is exotic and fearsome, but Fleming doesn't characterize it as a creation of a "savage race," as so many pulp fiction works had done.
Admittedly Bond is not particularly sensitive to the marginalization of black people in America, though to be fair Bond tends not to be sensitive to anyone's suffering unless he witnesses it personally. Still, a modern reader may take Bond's silence for agreement when he listens to two cops in Chapter 4 discuss what might be done about Mister Big. One cop wants to "take [Big] down to the Tombs and give him the works." The other denies this possibility, not out of any ethical objections but because he thinks Mister Big's influence is so pronounced that his mistreatment could bring about another race riot like the ones "in '35 and '43."
But here too, Fleming's main concern is probably to establish a level of verisimilitude appropriate to an action-thriller. If the reader should question why local American cops can't rein in Mister Big themselves, this sequence provides the answer, and shows why a heroic outsider is needed-- one who ends up conquering the villain not on American soil, but in the vicinity of the British possession Jamaica.
On a side-note, I find it interesting that Fleming relates in such casual fashion the idea that the New York cops routinely resort to inquisitorial torture, whether of blacks or any other suspects. There's a slight possibility that Fleming might have read James Baldwin's GO TELL IT ON THE MOUNTAIN, in which one of the minor black characters is subjected to such police brutality despite being completely innocent. The timing is rather close-- MOUNTAIN's publication date is 1953, while that of LIVE is 1954. Still, I don't think it's entirely coincidental that when Bond and Solitaire flee New York on a train bound for Florida, their porter is named "Baldwin."
Bond himself makes no untoward remarks about black people, American or otherwise, aside from those dealing with superstition, which as noted are rooted in the author's story necessities. Responding to M's imputation that Big is the first black supercriminal, Bond says that it's his impression black Americans are "pretty law-abiding chaps on the whole." When he and Leiter are captured in New York, he naturally fights the gangsters ferociously-- indeed, 007's hard-hitting escape from Big's goons is the hero's first spectacular action-exploit, given that he doesn't acquit himself all that well in CASINO ROYALE. Yet Bond resorts to no racial calumnies. The first American edition did eliminate one use of the n-word, though it appeared in the form of a place-name, not an epithet as such. If 007 is not particularly sympathetic to the plight of black people, he doesn't practice racism himself.
It may be argued that Fleming was hedging his bets: crafting a novel that might appeal equally to bigots, who wanted to believe in a black uprising, and liberals, who wanted to imagine black people as fully capable in any walk of life-- be it medicine, science, or crime (though Mister Big insists that he is an "artist," not a mere criminal). There's probably some truth in this. However, even if Bond evinces no "white guilt" over the history of slavery, he's fully capable of understanding racial loyalty and the burdens of history.
In Chapter 20, Bond imagines how Captain Morgan might have arranged the burial-site for his treasure by commanding a group of black slaves to dig a cave, after which Morgan then killed all the slaves to keep his secret. Then he thinks upon what might have happened when a modern black Jamaican discovered the treasure:
The Shark Bay fisherman who suddenly disappeared six months before must have one day found it rolled away by a storrn or by the tidal wave following a hurricane. Then he had found the treasure and had known he would need help to dispose of it. A white man would cheat him. Better go to the great negro gangster in Harlem and make the best terms he could. The gold belonged to the black men who had died to hide it. It should go back to the black men.The disappearance of the treasure-finder may suggest that "the great negro gangster in Harlem" may have rewarded the fisherman with death, but the principle of race-loyalty remains important both in LIVE AND LET DIE and in other Fleming works.
So to come back to the original question I posed, though I speculate that Fleming cared nothing about the sociopolitical success of black people-- for him, loyalty to his own race would have taken pride of place-- he felt that one ought to be able to care about "people of color" as much as anyone, on a one-on-one basis. I haven't touched on Bond's friendly relationship with Quarrel, the black Cayman Islander who trains him in snorkeling and whose life Bond saves, for one might argue that this is a friendship of convenience.
However, to reach outside this novel briefly-- two or three years later, during which time Fleming wrote his fourth Bond book, DIAMONDS ARE FOREVER-- Bond again showed that he could relate to suffering on a one-on-one basis. In that novel Bond, visiting a spa, is forced to stand helplessly by while two armed thugs punish a disobedient jockey by pouring hot mud in the man's eyes. Yet Bond is strangely less moved by the white jockey's sufferings than the pistol-whipping injury one thug commits upon a spa-attendant-- an attendant who happens to be old, fat, and-- black.