Echoing Donald.McLean's answer, Brad Bird talked about his inspiration in the artbook "The Art of the Incredibles". In short, there was no specific inspiring property that he's referencing. The film is about his own anxieties (his own mid-life crisis and fear of failure) mixed in with superhero and spy movie tropes from a hundred different sources.
It didn’t occur to me that there was anything personal about the
genesis of The Incredibles—a goofy story about a middle-aged superhero
and his family—until many years later, well into the film’s
production.
I first thought of the idea over a decade ago, when I had various
projects in development at studios all over Hollywood, but couldn’t
seem to get any of them made.
At the same time I was starting a family (with a wife, two young kids,
and a third on the way), and the twin demands of family life and
meaningful work were creating doubt in me that I’d ever be successful
in one area without failing miserably at the other.
I loved both, needed both, and couldn’t imagine life without either.
Consciously, I’d always thought of The Incredibles as a tribute to the
pop mythology of my youth, a gumbo of spy movies, comic books, and
favorite television shows; but I realize now that the other half of
its ingredients came out of personal anxieties about family, work,
expectations, and the special gifts we are all given but don’t always
appreciate.
Brad Bird - The Art of the Incredibles
Mark Cotta Vaz (film historian and the author of the artbook) who enjoyed considerable access to the film's creator/s seems to intimate that the main influence was James Bond, especially feature films like You Only Live Twice
The Incredibles was not only a metaphor for Bird’s personal struggles;
it proved to be another chance for him to turn the dials on his
antennae and draw out of the ozone the free-floating dream stuff of
pop culture, as he’d done with The Iron Giant (which celebrated
everything from Superman comics to cheesy science fiction monster
movies). Incredibles design schemes ranged from a stylized take on
human and superhuman characters to the aesthetics of early James Bond
production designer Ken Adam to the distinctive sixties notion of the
future. The innovative but reverential Incredibles vision also pokes
self-aware fun at the requisite supervillain’s lair and at haughty
supervillains who’ve captured a nemesis and can’t resist gloating
(it’s called “monologuing”). One of the film’s classically influenced
environments is the exotic island where evildoer Syndrome plots the
downfall of our hero, Mr. Incredible.
Mark Cotta Vaz - The Art of the Incredibles
As to why they had the particular powers they had, these are largely extensions of their personalities rather than intended to reflect a particular comic-book family or power team
Once I had the idea for the film, I quickly realized I wasn’t as interested in the superpowers as in the characters themselves. I decided to base the powers on the personalities of the characters. Traditionally the father is the strong one in the family, so Bob’s power is super strength. Helen as wife and mother is being pulled in many different directions, so she seemed to be somebody who could stretch and contort without breaking. Violet is an insecure teenage girl who doesn’t want people to look at her, so she gets to become invisible, and because she’s a little insulated and protective, she can project this force field. Young boys are hyperactive and have enough energy to power a small village, so I decided to make Dash really fast. The baby, Jack-Jack, has no known powers, so he’s all unformed potential. When I thought along those lines, things fell into place fairly quickly
Brad Bird - The Art of the Incredibles