Hi, Hibiki,
It’s not impossible to add keys to a PVC-pipe flute. For instance, the first “one-key”, Baroque flute was made way back, in about the year 1695, so making a key need not be a “high-tech” effort!
To make a key, you’ll need a small piece of thick sheet metal. The metal can then be cut into rough shape with the use of a simple jeweler’s saw, a miniature version of an ordinary plumber’s hacksaw, and once you have the key cut into rough shape, the key could then be finished by the use of a file and/or a grinding stone, etc.
The key will then need to pivot, so it’s necessary to drill a very small hole through it, from one side of the key to the other. This could be done by putting the key into a vise, and then drilling through it while being careful to keep the hole centered through the metal. Once that’s done, any excess metal could then be removed from the key, say, away from that pivot point and towards the ends of the key, again by the use of a file and/or a grinding stone.
The key will need something to pivot on, and there are two common ways to accomplish this, 1) by adding “posts”, which is more difficult, or 2) by adding a “block”, which is relatively easy. I’ll leave it to you to figure out the posts, but for now I’ll suggest an easy block configuration, numerous examples of which can been seen on “early” flutes. In short, and this is more of a “repair” technique but will suffice for the purpose (BTW, the making of a flute including block(s) is another matter altogether), a block could begin as a simple “cube” of the same material as the flute is made of, and then could have one side of that cube shaped as a curve, again by means of a file and/or a grinding stone, such that the curve then fits to the cylindrical shape of the flute. The block is then glued onto the body of the flute, and is then “split” into two parallel blocks, again by means of a file and/or a grinding stone, where the split is equal in width to the width of the key. Alternately, two pieces of material could be glued on, such that they are both parallel and are spaced at the width of the key.
Once that’s done, a very small hole will need to be drilled through the parallel blocks, to hold a pin, a pin which just fits through the key and the blocks. This is the pivot.
The key will need a spring, and here there are a variety of alternatives, but perhaps a slender strip of hacksaw blade could do, as hacksaw blades have a spring-like quality. Attaching the spring to the key could be a challenge, where perhaps it could be riveted on, glued on, or even screwed on, but soldering, and such heat, could remove the spring-like quality of the spring. And, there are other ways to attach the spring, for instance.
The key will also need a pad, to seal the hole, and leather is a traditional material, but a layer of silicone might work just as well.
The key might also need to be bent into final position, including being shaped to the curve of the flute, by means of smooth-jawed pliers, so as not to mar the finish of the metal. Now, if you don’t have smooth-jawed pliers, ordinary pliers could have a bit of brass sheet wrapped around each of the jaws, and the same could be done for the jaws of the vice as used in drilling the hole through the key.
Of course, all of this assumes that you have determined the correct size and location of the necessary tone hole!
No doubt, I’ve left out a number of details, here, but seeing as you are a musician, I’m going to leave the above ideas to your imagination, and I’ll be here to further discuss the matter, if you like.
Edits: Dang! Dontchajusthateit when the keyboard screws up (yeah, yeah, blame it on an old, and somewhat dysfunctional keyboard)! 
