One-man show relives theater history; Edmund Kean. Play by Raymund FitzSimons. Starring Ben Kingsley. Directed by Alison Sutcliffe.

A formidable histrionic display by Ben Kingsley, an angled glimpse of some 19 th-century theatrical history, and a self-obsessed reminiscence by a self-destroying superstar - such are the ingredients of ''Edmund Kean'' at the Brooks Atkinson Theatre. The Academy Award-winning actor (for ''Gandhi'') has brought Raymund FitzSimons's one-man drama to New York in a production that appears to capture all of the flair and flourish that dazzled London audiences.

Mr. FitzSimons has fashioned an entertainment in which Kean serves as narrator-autobiographer and sharp-tongued commentator. As the meteoric comet of his own account, Kean early on points out that his star didn't begin rising until he had spent most of a decade as a frustrated provincial acrobat-dancer and struggling player before his first Drury Lane triumph on a snowy January night in 1814. The success was cruelly marred by the recent death of his four-year-old son.

In the FitzSimons dramatization, Kean remains haunted by the harlequin apprenticeship when he sang and danced and rattled his tambourine and frequently starved along the way. Meanwhile, the raw young vagabond was inventing the imaginary aristocratic background with which to conceal the actual wretchedness of his beginnings and early life.

As Kean tells his story, describes the plots that ''they'' are concocting against him, and heaps scorn on the aristocratic milieu to which his talents have gained him access, he slips in and out of the roles that have made his reputation. In the process, Mr. Kingsley presents a 20th-century actor's view of a 19th-century stage phenomenon. Beginning with the Shylock that conquered the Drury Lane audience of which Hazlitt was a member, the roster includes Macbeth, Richard III, Othello, Hamlet, Timon of Athens, and Lear, among others. The interwoven excerpts are relevant and often illuminating, even such self-serving quotes as Lear's ''I am a man more sinn'd against than sinning.'' Mr. Kingsley delivers them with power and authority.

Kean's very public private life unfolds as the actor boasts of his alcoholic and amatory exploits. Once having captured the crown as England's greatest tragic actor, he lets it slip through his fingers - not because of hostile conspiracies, but because of his own intemperance and rash behavior. The present brief chronicle ends with the ominous farewell appearance in ''Othello,'' in which Kean as the Moor collapses and implores Iago, played by his son Charles, ''I am dying - speak to them for me.''

Mr. Kingsley switches mercurially from onstage role playing to the confessional exposition that fills out the bustling two-hour traffic of the piece. ''Edmund Kean'' is a play about the mystery of talent and its sometimes flawed human embodiment. As staged by Alison Sutcliffe (Mr. Kingsley's wife), it presents a fascinating portrait of a man who rose from obscurity to the pinnacle of fame, who yearned for esteem and scorned respectability, who kept a pet lion, who compared himself to Byron and Napoleon, and whose accomplishments could not survive his excesses. In the end, a broken actor, Kean personifies the mythic figure of Shakespeare's imagery - ''a poor player/That struts and frets his hour upon the stage,/And then is heard no more. . . .'' All of his defiant mockery and bravado have been dissipated. Never a sympathetic figure, he becomes pitiable, or at least understandable.

The production has been well designed by Martin Tilley to suit the needs of the work. A small, footlighted stage, hung with drapes, also serves as the actor's dressing room. There are a chair and a makeup table and two well-used trunks, the essential baggage of the strolling player's life. John Watt's lighting enhances the mood of bygone theatricalism and occasionally focuses a shaft of high incandescence to silhouette Kean in a striking attitude.

Apart from quick costume changes and a few touches of face-blacking for Othello, Mr. Kingsley relies for his characterization on the actor's skills and resources. Occasionally, he impersonates Mrs. Kean and a few of the other principal persons in Kean's life and career. But not very often. After all, even the most important of them are walk-ons and incidental players in Edmund Kean's scenario.