As palaidn:

Rage of Halone strength debuff will ALWAYS be up, avoiding that means you don't want a Paladin there.
Blind from Flash will often be up, although not always, and can be avoided if asked.
Silence will be up every now and then for 1 second, although it can be avoided if asked.
No-WS will be up very often for a few seconds each time, although it can be avoided if asked.
Circle of Scorn will be up every so often, although it can be avoided if asked.
Knock-down will appear whenever you ask the paladin to interrupt, although it can be avoided if the Paladin never interrupt anything.

So in the extreme case, the Paladin can perform reasonably close to maximum capacity with 1 debuff.
For the Paladin to perform at full capacity, he needs to have access to 6 debuff slots.

Although I think Blind, Silence, No-WS and Knock-down may all be shared categorical debuffs, maybe people who do FATEs can check if you ever see double Blinds up?

If these are categorical, then Paladin needs minimum 1 slot, and to perform at full capacity needs 2 slots plus 4 shared slots.