I have a Samsung Note 4. My wife just got the Samsung J7 . Both came with fast chargers. Mine charges up just fine on both the fast charger and a conventional 2.1 amp charger, albeit quicker on the former. The conventional 2.1 amp charger has little or no effect on my wife's J7 but the fast charger works as expected . Is this normal ?

That doesn't sound normal to me. I have an S7 with the fast charger and gave my S5 to my son to use.

Both the fast charger and the older style charger charge my S7, but the fast charger is very quick while the older charger will take a lot longer.

I have also tried the fast charger on my old S5 and it charges, but at a normal(slower) rate.

I would recommend having your wife's phone checked out where you bought it to see if it is defective.

Perhaps she has a bunch of stuff running in the background and they're using the slow amount of charge the slow charger is giving it?

No, that's not normal. Even a 1 amp charger should have some effect, let alone one putting out over 2 amps. Something is using a lot of power.

An app like AccuBattery might be helpful.

Try to use the cord that came with the J7 on the 2.1A block and see if it charges normally. It still wouldn't be fast like the fast charging block but the cord can make a real difference.