The highest possible permanent Spell Save DC is 28
The Character
Chad is a Level 17+ character with at least one level in warlock and these magic items:
- Robe of the Archmagi
- Rod of the Pact Keeper (only applies to your warlock spells)
- Ioun Stone of Mastery
- Tome of Leadership and Influence
The Calculation
+8 | Base Score
+6 | Level 17+ Proficiency
+1 | Ioun Stone of Mastery (Proficiency increase)
+2 | Robe of the Archmagi
+7 | 24 Charisma (acquired in specific Adventure Module, see below if okay with spoilers)
+1 | +2 Charisma (Tome of Leadership and Influence1)
+3 | Rod of the Pact Keeper
This involves...
[the Maze Engine from Out of the Abyss (188) which says:]
On each of the engines turns, roll a d100 and consult the Maze Engine Effects table to determine what the engine does.
[...]
36-49 | Loud whispers emanate from the hollow interior of the engine. Each character in direct contact with the engine can increase one ability score of his or her choice by 2, to a maximum of 24
Rulings
1 You can only use one Tome/Manual of any one kind on a character in Adventurer's League (DDAL FAQ v7.1 p. 8)