I'm certainly not an expert, but from what I understand, the type of observation done in helioseismology might not work with gas giants, hot jupiters, ice giants, etc.
The sun is dense enough and it has enough gravity that, while its a plasma, it's relatively solid most of the way through. Unlike Red Dwarf stars which are lighter and undergo convection (0.35 solar masses and under are modeled to be fully convective), the sun is layered and doesn't undergo convection.
While oversimplified, the sun behaves like a drum in regards to it's internal soundwaves. The sun is also very very loud, inside and on the surface.
If you played a drum in a vacuum, you couldn't hear it, but you could observe the motion of the drum's surface and work out what it would sound like by visual observation only. Same with guitar strings. The vibration is visible in wavelength and amplitude.
Exaggerated, the pattern on a drum would look something like this.
Source of picture.
That's basically how the Sun's soundwaves are studied. It's often compared to Sonar but I don't like that comparison because sonar works by sending a soundwave out and seeing what gets reflected back. It's more like the visual observation of sound vibrations, or, like studying a drum by looking at it's vibrations instead of listening to it.
This is a picture of what those vibrations look like on the sun (again, greatly exaggerated).
As noted in the article, a drum has one node. The sun has many nodes, so it's more complicated. It's the studying of those many nodes that gives insight into the inside of the sun.
The problem with doing that on a gas giant planet is, (and I'm partially guessing here), I don't believe a gas giant planet is solid enough to behave like a drum. The convection (and gas giant planets are full of convection in their upper layers) would likely dilute any studyable patterns or nodes from it's interior, much like how wind reduces sound waves. I don't believe this method would work on gas giant planets.