Will gold leaf adhesive work on flexible TPU plastic?
I've never tried to gild a phone case before, so take this with a grain of salt...

I would suggest using the same methods you'd use for exterior gilding: prime the surface with several layers of primer, sanding in between; apply an exterior-grade gold size (also called "oil size" or "solvent-based size"); wait for the size to dry to the appropriate level of tackiness; apply the metal leaf; after a bit more drying, brush off any loose gold; after allowing the size to fully cure (could take a week or more), apply a sealer to prevent tarnishing.

If you don't want to go to such extremes (trying to buy oil size in quantities small enough for your purposes would probably be difficult), it might be sufficient to use primer + your existing gold adhesive (probably PVA-type) + leaf + varnish/sealer. For the primer, try to find a paint that's specifically meant for plastic: you want something that's guaranteed to stick to the plastic, and then your gold adhesive will stick to the paint (or at least it should), and then the metal leaf will stick to the gold adhesive, and then (after everything has cured as fully as it ever will, but before oxidation has set in) seal the metal leaf both to protect it from abrasion and to prevent tarnishing.

Regardless of what specific steps you follow, you may end up with a phone case that's noticeably thicker than it was before. Make sure to mask off any areas that shouldn't get thicker, i.e. any prongs/thingamabobs that make the case stay on the phone, the inside of the case, the holes for the camera/power cord/headphones/switches and buttons, etc.

The other caveat is that, unlike IKEA furniture, your phone case is probably not flat. This means that you will be gilding around a curve, which is more difficult than just covering a rectangular flat area. You will end up with gaps, and even after doing your best to fill them in, you'll see the seams, and some gaps will just be too small to fill but not small enough to be invisible. (This is where genuine gold leaf would make things easier: it will stick to itself, allowing you to fill in gaps totally invisibly.) Depending on the effect you want to achieve, choose your primer and/or adhesive color to either contrast with the gold (a red Armenian bole color is traditional for this) or blend in as much as possible (i.e. yellow).