I had my first flat on my bike after about 10 months of riding it, so I get a thick thorn protector tube and put in a cut up of the old tube for an extra layer of protection, and about a week later, the tube tears right at the valve. I rinse and repeat, and two weeks later it happens again, exact same thing, same tire, the back tire.

I make sure it's facing straight out from the tire when I fill it up, and right before riding it the time it went flat, it was sticking out straight, but when it was flat, it looked like it had done some sliding and rubbed against the rim, it wasn't even close to sticking out straight.

Can too much or too little air be the cause? How do I figure out if it has the right amount of air? I don't have an air-pressure checker, but I might end up getting one. Can breaking cause this? This is a gear-less bike so the feet do all the breaking.

Attached is what I'm trying now, just a regular tube with the extra layer of a tube from a past flat. The thick tubes that went flat also looked like this.

My first guess is 'too little tire pressure.' Too little pressure means the tire and tube are not pushing as hard against the rim, and so can slide around a bit due to the force put upon the tire by braking and accelerating.

To what pressure are you filling the tire and are you using a pressure gauge? And what size of tire is it?

Flats are a normal part of riding. One flat in 10 months may not justify the compromises associated with your belt and suspenders approach to flat protection. But if it makes you feel comfortable, go for it.

Yeah, one flat in ten months shouldn't justify all this malarkey. They're just an occasional part of cycling; live with it.

+1 on too little pressure.

Particularly foldable tires can slip at low inflation.

If you really want to avoid this situation, use tubular tire glue(or contact cement) to glue one side of the tire to the rim.
It'll be plenty to keep it from sliding, and you can still remove/insert the tube from the other side.

Use tubes with threaded valve stems and thread the nut against the rim (finger-tight only after you pumped it to the nominal pressure)

^...after first poking the valve into the tyre to ensure its base isn't jammed under the bead.

most flat tires on bikes come from mounting the tube and tire wrong,,,the tubes get folded or have dirt or the valve stems arent lined up,,,,. Just be carefull in mounting it,,when a new tube is put in,,,you air it up then you let most of the air out so all the folds and creases come out,,then make sure the valve stem is lined up straight before you make the final air up. Make sure the beads are seated properly almost everytime I buy a bike the tire beads are not seated. If they are not evenly seated let the tire down,,lube it with soapy water and air it up again. A tire properly mounted will not shift on the rim,,even if the pressure is a little low. Howie(40 years in the tire business)

Oh yea I wouldnt use thick or puncture resistant tubes,,they are gimmicks that cause more trouble than they are worth