'distinctive legacy' is a perfectly correct and usable phrase in written English.
It typically refers to something inherited from the past that is notable or powerful in some way. For example, you might say, "The distinctive legacy of the ancient Egyptians can still be seen today in the form of their monuments and pyramids."
The presidents will each leave distinctive legacies.
Homes built along the lanes, the narrow passageways called lilong, or longtong in Shanghai, are the city's most distinctive architectural legacy of the late 19th century and early 20th.
Radio Centre supports the closure of 6 Music and generally welcomes the BBC's aim of refocusing its radio services, but said the station's distinctive "John Peel legacy" programmes should be broadcast on Radio 1 and Radio 2. Value Partners suggests that, as an alternative, 6 Music could be privatised.
And this applies most particularly to the highly distinctive work and legacy of Professor John Anderson, the dominant force in philosophy at Sydney for much of the twentieth century.
The West did not react to the wall with escalation, but held firm for 28 years until it prevailed: that was the only way forward now, she suggested.For all the new activism, German foreign policy still has distinctive features, mostly legacies of a culture of atonement.
American experimental filmmaker David Lynch's bizarre, addictive TV show "Twin Peaks," which aired from 1990 to 1991, is beloved for a lot of things, but its music is arguably one of the most distinctive parts of its legacy.
Jaguar's distinctive all-aluminum chassis (another legacy of the Ford era) significantly reduces the car's weight and gives it a performance advantage over the competition.
Since 2005, Schaffner has lived in Tyng's former house, which had been substantially transformed by the architect, a distinctive rarity considering her poignant legacy of unbuilt projects.
