I'm making a Bladesinger (Wizard)/Swashbuckler (Rogue) Multiclass.
Can the Rogue's Uncanny Dodge class feature be used at the same time as the Defensive Duelist feat?
Each of them uses your reaction, which is a part of the "action economy" for a round/turn in D&D 5e. You get one reaction each round; choose which one of these you want to do: the Defensive Duelist feat, or the rogue's Uncanny Dodge.
The Defensive Duelist feat (PHB, p. 165) says:
When you are wielding a finesse weapon with which you are proficient and another creature hits you with a melee attack, you can use your reaction to add your proficiency bonus to your AC for that attack, potentially causing the attack to miss you.
The rogue's Uncanny Dodge feature says:
Starting at 5th level, when an attacker that you can see hits you with an attack, you can use your reaction to halve the attack’s damage against you.
You can only take one reaction until the start of your next turn:
When you take a reaction, you can’t take another one until the start of your next turn. If the reaction interrupts another creature’s turn, that creature can continue its turn right after the reaction. (Basic Rules, "Reactions", p. 73)
If you are pretty sure that a slight boost in AC will render the hit a miss, use that one. Zero damage is better than half damage.
If a boost in AC won't stop it being a hit, use the class ability to halve the damage.