Actually it is possible. The toy would need to have a cavity such as this. Fluid pressure applies a force over an area. The thin tube that runs down the toy has a small cross sectional area, so therefore the force expanding the toy outward would be small. The head of the toy has more area for the pressure to act upon and therefore would have a greater force being applied to expand it outwards. Not only that, the thicker material of the shaft would work against the shaft expanding, while the thinner material of the head would allow for the head to expand. This exists too in other toys. There are dog toys on the market with inflatable knots.
It wouldn't be a "flare", it would be a round swollen bulb. Fluids expand by path of least resistance. When trapped within a pliable shell that means a sphere. You couldn't prevent the surface of the head from expanding along with the sides. An inflatable dog "knot" works because it's at the base, where the shaft will above and below will cause just the sides to expand, but even then it's not an accurate knot, a knot is not a symmetrical sphere around the base of the shaft, it has discrete lobes.
Then have a conical cavity. I didn't post this to debate how it would work, I want to know if it has been done.
And the answer is, no, it hasn't been done, because it can't work.
Must be good for stretching you out ?
