BAB, Hitpoints, Saving Throws, and skill points from classes always add, they don't overlap.
So you get the +5 BAB from your Paladin class levels, and the +1 BAB from the Hell Knight Commander level, to have a BAB of +6/+1 (i.e. BAB of 6 and that triggers the 'second attack at 6 BAB' rule, so you get another attack on a full attack action, at -5 to hit - so +6/+1 (one attack at +6 BAB and one at +1 BAB)).
You also add the saving throw numbers together to get your base saving throws, and add your paladin and hell knight commander levels to get the max ranks you can have in a skill etc.
The numbers on the class progression are already added together for you - each Paladin level adds +1 BAB, so on the class table at level 5 it has the BAB listed as '+5'. If you multiclass, though, you need to add the numbers together yourself - so you find the appropriate numbers for the amount of levels you have in the class on the table for each class, and then add those numbers together manually on your sheet.
Levels are modular, basically, each single level gives BAB, hitpoints, skill points, saving throw increases, so forth, and those always stack. The class progression table just adds the numbers together for you, and displays what you get at each level of the class if you take that class and no other.
It can be confusing, but is intended for ease of use, and not to penalize multi-classing.