Is it legal to bring your own survival gear aboard an airliner?
Yes, it's legal to bring a parachute, if you can fit it within the permitted carry-on limits. It has been done.

No, it's not going to save you. You are not going to be able to jump out of an airliner. Unless your name is D.B.Cooper, and you're hijacking the last flying 727 with a rear exit door, that is. Again.

No, it's not legal to bring a pressurized container onboard a passenger jet. When you want to fly with a pressurized tank (say, a pony or deco bottle for tec diving), you have to unscrew the valve and bring it separately. This is to ensure you can't bring explosives or poisons inside the tank.

Yes, if you could bring an oxygen or nitrox container (less fire hazard than pure O2), combined with a firefighter SCBA, it could improve your odds of survival in the very marginal event of a fire-related accident, in which the plane manages to land intact enough for you to don it.

No, none of these are practical measures. If you want to somewhat improve your odds without impractical means, wear comfortable leather shoes without heels, cotton clothing, and a fanny pack for your papers, so that you're not tempted to reach for your luggage in an emergency.

One specialized item that has been considered for inclusion on airliners as safety equipment is fire hoods. There are portable smoke hoods that can give you a couple minutes' protection for evacuation. They don't include air or oxygen, only a simplistic filter, which is still a solid step above just holding your breath.