Nintendo is rarely, if ever, the first at anything, and I don't think many are still under any of those delusions anymore.
Instead, Super Mario 64 is simply noteworthy for the camera, and just being an all around amazing game.
That said, I can definitely see a lot of Jumping Flash was incorporated into SM64.
A) Actually, they were. Nintendo were the first to make a truly side-scrolling game, and pretty much innovated the concept of a "platformer". They were the first to have a "go anywhere" type of adventure game like The Legend of Zelda. They were the first to have a non-linear, horizontal and vertial scrolling action game like Metroid. They were the first, to my knowledge, to incorporate permanent power-ups/upgrades to their characters (outside of traditional rpgs), in Mario, Zelda and Metroid. They were the first company to use the "d-pad" directional controller design, as well as standardizing the idea of "dpad, start/select/ A and B buttons", etc. They were the first to feature L and R shoulder buttons on a controller, and the basic design of the SNES controller was emulated by basically everythin that came after, including the PS1, Dreamcast, Xbox, you name it. The N64 controller introduced the idea of a home console controller having both an analog stick, a "trigger button", and the controller rumble feature (with the rumble pack). There are a great many things Nintendo have created or innovated, including such things as the "kart racer" genre with Mario Kart, and the "party fighter" genre with Smash Bros. Not to mention they were the first to incorporate true touch pad or motion controll input into gaming, both of which others have blatantly copied since.
B) Mario 64 was not the FIRST attempt at a 3D game, but Mario 64 perfected it. And there is no way that they could have borrowed ideas from Jumping Flash, when Mario 64 was in development before JF was, in fact it started as an FX-chip powered SNES game concept. There were other games before JF that attempted 3D gameplay, but none of them, JF included, were able to really get it "right". The remarkable thing about SM64 wasn't merely the camera, which was notable, but it was the sheer level of control and mobility that you had over your character, and the interactivity in the 3D game world, jumping off walls, picking up blocks, crawling, doing backflips to reach higher areas, etc.