As a player who has probably a better appreciation for rapidfire weapons then average, even I have only ever used chainfiring mode with Master Ammochain - and even then mostly only on deep Ao666 floors where I can spawn into a horde of nasty stuff all on my screen at once.
Other then that, it has no use and no synergies of which I am aware - Cateye and Entrenchment both look in theory like they would benefit from it, Cateye because you can see more to chainfire at safely, and Entrenchment because it specifically benefits from being in chainfire mode, but in practice, anything other then a minigun will need to be re-loaded long before you can do much(note that with Entrenchment, stopping to re-load leaves you exposed to all enemies at the exact moment your bonus resistances vanish without a trace - IMO, Entrenchment would only be viable if it maintained its resistances during reloading a rapidfire weapon as well as well chainfiring it, and then only if it also speeds up reloading and stops/reduces knockback[whereas Cateye is very useful regardless of your weapon choice]). Even with a minigun, it's so ammo-consumptive that it makes very little sense to use - in almost all cases, normal bursts would be more effective. If they're not, you might want to re-think the build you're using for rapidfire weapons.
Ammochain, of course, solves both of these problems, because every burst costs only one round, whether you're concerned with your magazine or with your backpack.
