I believe you get the same 8 slots you'd get if you bought them separately - 4 for Prophecies, 2 for Factions, 2 for Nightfall) But anyway, you're not going to get 8 (or 10) more slots. Just like when you add any key to your account, you will only get the stuff you don't already have.
So, if your current account only has Prophecies (for example) - which has 4 slots - you'll only get 4 more slots (2 for Factions, 2 for Nightfall) because you already have the 4 for Prophecies. If your current account already has all 3 campaigns, you won't get any extra slots at all - you'll only get any bonus material (weapons, mini-pets, the extra 2 slots?, etc.) that come with the trilogy.
As an unrelated side note - you get more storage space by buying a extra character slot and using it as a mule (when equipped with beltpouch & bags), than you do by buying an extra storage pane.
The Trilogy has one key for all content - Prophecies, Factions & Nightfall. You enter the key once and have immediate access to all three games. It gives you a total of 8 character slots. The Trilogy does not include Eye of the North.
You also get M.O.X. and the Fire Imp as bonus. The Prophecies included is the Game of the Year edition which includes bonus weapons.
I'd Imagine 8 slots. 4 from Prophicies, 2 from Factions, 2 From Nightfall. Just like how if you bought the first, 2nd and 3rd games chronologically when they were released and added them to your account.
Btw, don't expect to add the trilogy key to your current account, I don't think that works.