I am at the moment playing 3.5 and in a discussion with my dm he told me that the increase in attack bonus granted for each level in a prestige class only applies to the first attack. For example, a 5th level fighter/1st level duelist would end up with a BAB of 6, with no second iterative attack instead, rather than the expected 6/1. His reasoning for this is that no other attacks are listed via the tables, so the character doesn't get them. I can see no reference to this anywhere else, however, and it doesn't make much sense.
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Your DM is WRONG.
Iterative attacks in 3.5 are purely a function of increasing attack bonus. For every 5 points, you gain another attack. Thus, when you reach a BAB of +6, you can, with a full attack action, make two attacks at +6/+1. At +11, you can make three attacks, at +11/+6/+1.
With regard to stacking, the D20 SRD is quite clear:
Prestige classes are, in this case, no different from any other class. If you have a BAB of +7 from 7 levels of Duelist, and a BAB of +9 from 9 levels of Fighter, they would stack to a combined +16, giving you four iterative attacks, at +16/+11/+6/+1.
Keep in mind of course, that iterative attacks are only available as part of a full round, full attack action. In other circumstances, such as after a move action, you would of course, be limited to only one attack with your full BAB, i.e. at +6 in your example, or +16 in mine.
The rules for prestige classes follow the rules for normal level advancement. You simply add the BAB (and saves, etc) from the prestige class table to the one from your starting class.
Your five levels of fighter give you a +5 BAB, and your first level of Duellist add a +1. Therefore, your BAB is +6.
There is no rule that the BAB from your prestige class stats only count for a specific attacks; you can use it for every attack.
A discussion with almost the same example as yours can be found on the paizo forums.