I'm new to having a camera and I'm not sure how everything works with
Just basic advice, but before buying anything, I'd say practice enough to be comfortable with using your camera. Bad technique will follow you to near gear, and getting a new piece of equipment can exacerbate the complexity of the picture when you're learning.
I have a T6, and I would like to take pictures with flash without the
kids squinting and that it is fast when I shoot.
The way flashes work is that they use a large capacitor to release a ton of charge all at once to fire off the flash tube. That capacitor takes time to "fill" from the batteries. So, trying to burst shoot in rapid succession may not be possible, given how long it can take the capacitor to "refill". The only way to get the flash to be ready faster is to shoot at lower speeds and not use up all the charge at once. So, you may need to increase iso or aperture.
To keep the kids from squinting, I'd actually recommend not using direct flash, but to get a hotshoe flash (speedlight), and bounce it (aim the head at a reflective surface, like the ceiling or wall), and use the reflected light as your illumination. Flagging off the head so there's no direct light will also look more pleasing, as well as avoid blasting someone in the face with the light.
A used 580EXII or a Godox TT685C (at the time of this writing) aren't too expensive and good solid flashes. But the TT685C is better if you think you might do off-camera lighting setups, because it has radio triggering built-in. See also: What features should one look for when selecting a flash?
I am not sure how I should be choosing the lenses.
It may be too early to consider buying a lens if you don't know why you want a new lens.
Lense have two main specs: the focal length and the maximum aperture. The focal length affects the magnification and field of view; the maximum aperture affects the depth of field and limits how fast your shutter speed can be without adding flash. When shooting portraits, most folks favor a slightly telephoto prime lens, such as a 50mm f/1.8 or 85mm f/1.8; but you can also just use the 18-55 kit lens until you figure out what it is about it you'd most want to change for portrait shooting.