This is an odd question, but I'm sure it must be doable.
The main ways I've found so far are:
- using polymorph, shapechange, etc to directly turn into something that has the swallow whole ability.
- having the anthropomorphic animal template from Savage Species. This only has level adjustment given for a preset list of animal types, but this seems to be only a space-requirements limit (e.g. an appropriate LA could be eyeballed for others). The (non-dire) animals that have the swallow whole ability that I can find are:
- 3.0: giant toad (Oriental Adventures), poisonous toad (Oriental Adventures)
- 3.5: allosaurus (Monster Manual II), battletitan (Monster Manual III), cave tyrannosaurus (Miniatures Handbook), cryptoclidus (Monster Manual II), forest sloth (Monster Manual II), legendary shark (Monster Manual II), megalodon (Monster Manual II), mosasaur (Stormwrack), spinosaurus (Monster Manual II), tyrannosaurus, quetzalcoatlus (Monster Manual II)
- Pathfinder: giant frog, giant snapping turtle, giant toad, megalania, tyrannosaurus
- Pathfinder, third party: giant chameleon, giant frog giant pike, giant snapping turtle, giant toad, gulper eel
- being a dragon of Huge size with the Snatch and Swallow feat. You might qualify for this by:
- being a kobold with the Dragonwrought feat, and somehow permanently becoming Huge size.
- repeatedly changing into a Huge dragon (via polymorph effects, Draconic Wild Shape feat, or the Master of Many Forms class), allowing you to gain the feat but it only working while you're a Huge dragon (depending on the DM).
- being a 9th-level synthesist summoner with the swallow whole, grab, and bite evolutions.
- being an amphi dragon, wyrmling (Tiny, 1 HD, LA +2), very young (Tiny, 4 HD, LA +3), young (Small, 7 HD, LA +4) or juvenile (Medium, 10 HD, LA +5), from Dragonlance: Bestiary of Krynn Revised. This is less of an option if you don't want to be covered in warts, constantly produce a repulsive smell, and naturally generate enough acid to put holes in even stone floors.
- using the 8th-level spell bite of the king (Spell Compendium) for a single pseudo-swallow whole attack. This is only available with the Gluttony and Hunger domains.
However, I'm still curious to find more "elegant" ways this might be done, with a minimum of template use and questionable rules interpretations. For example, there might be a monster type out there that I've missed that has level adjustment listed and already has the swallow whole ability, or there might be a class or prestige class that can get it directly in some way. (The summoner can, for example, but it's still not exactly the summoner getting it, but only getting the benefit of it via the synthesis ability.)