Human training. Bene Gesserit training. Mentat training. Fremen training. And finally, the powers of the Kwisatz Haderach. 

This class tries to show all these abilities, making it overpowered. The mental process I've followed to balance it is this:

-"The spice must flow" feature. A single level is already cripling (specially since skill checks are the main focus of this class).

-You are good at fighting, but not as good/flexible as a College of Swords/Valour bard. The AC bonus might be too much; I added it as a conditional reward for keeping it real.

-You are good at magic, but not as good/flexible as a College of Lore/Eloquence bard. Divination is not really the best magic school, and the spells added are cool but not inhrently broken.

-You are good at skill checks... Maybe too good. This is balanced around the replaced bard features and the idea that sometimes you'll fail the "The spice must flow" saving throws.

-You are good at buffing you allies. Maybe TOO GOOD starting 6th level. Using Bardic Inspiration as a reaction is very cool, but in an already overloaded subclass this is plainly broken. 1d6 psychic damage and the urge of using it that turn make it just a little less broken, but broken nonetheless.

Muad'Dib

At 3rd level, the bard starts to learn the different ways of Paul Atreides training. This feature replaces the bard Expertise feature.

Foundational human training: you gain the Dueling fighting style. As long as you have a light weapon in your main hand, your off hand is empty and you have no armor, you gain AC equal to your Charisma modifier. If you are using a light armor, this bonus is halved.

Mentat training: you gain proficiency in insight skill checks. You can add double your proficiency bonus if you are already proficient in it.

Bene Gesserit training: you add the command and the detect thoughts spells to your spell list.

Fremen training: you gain proficiency in survival skill checks. You can add double your proficiency bonus if you are already proficient in it. You gain desert as a favored terrain.

Usul: whenever an ally rolls a 1 in your Bardic Inspiration die, they dont lose it.

The Spice Must Flow

Starting at 6th level, after every Long Rest, you must consume Spice. If you dont, you make a constitution Saving Throw (DC= 12 + the number of long rests without taking spice). If you fail this saving throw, you get a "Spice Withdrawal" level. It works exactly as an exhaustion level, but it can only be removed by consuming spice. Consuming spice removes every level of "Spice Withdrawal".

Spice is a consumable that might be bought from merchants or found in the wild via survival checks (DC=20). Its easier to find in desert terrain (DC=15). Consuming spice grants advantage in mental skill checks for 1 hour, unless consumed by a College of Atreides bard.

Lisan al-Gaib

At 6th level, you deepen your training.

Foundational human training: as long as you have a light weapon in you main hand, your off hand is empty, and you are wearing light armor or no armor, you get an extra attack and an extra reaction.

Mentat training: you gain proficiency in investigation and perception skill checks. You can add double your proficiency bonus in any of them if you are already proficient in it.

Bene Gesserit training: you gain advantage in constitution saving throws made against poisons. Once per long rest, you can use one spell of the Enchantment school without spending an spell slot.

Fremen training: you gain proficiency in animal handling and stealth skill checks. You can add double your proficiency bonus in any of them if you are already proficient in it. 

A Terrible Purpose: you cannot gain inmunity or resistance to psychic damage.

Mahdi: whenever an ally within 30 feet makes an ability check, a saving throw or an attack roll, you can use your bardic inspiration on them as a reaction. If you do, you take 1d6 psychic damage, and the bardic inspiration expires at the end of this ally turn.

Kwisatz Haderach

At level 14th, power of the Kwisatz Haderach awakens. This Feature replaces the Jack of All Trades bard feature.

Prescience: you gain the ability to use spells of the Divination spell school without spending an spell slot, as long as this spells are level 5 or lower.

The Golden Path: you cannot be surprised. 

Genetic memory: you can add your proficiency bonus in skill checks you are not proficient in. If you make a skill check you are already proficient in, you make it with advantage.

Voice of the Outer World: whenever you spend a Bardic Inspiration charge, all allies in a 30 feet radius gain temporary hit point equal to your Charisma modifier.