If you're a long-time D&D/Pathfinder gamer, you're familiar with creative familiars and animal forms. Parrots who can talk, monkeys who can carry things around, legendary gorillas who circumvent normal strength maximums while wielding items without restriction...
This came up last session, so I needed to spend a little effort researching whether Talking Parrot Familiars were a part of 5th edition.
Executive summary:
1. Wizards can't speak through their familiars using rules as written.
2. Familiars are significantly weaker than previous editions.
3. You can create a spell to speak through your familiar (or companion).
Analysis:
Parrots on their own will say nonsense phrases, not meaningful speech.
At this time Familiars do not gain INT, so the Parrot is locked at 2 INT. (spell details below)
N'Krumah's Faithful Companion spell is very like Find Familiar but avoids the "permanent but dismissable at will" Familiar bond, and there seems to be no feedback effect in 5ED anyway. Perhaps you could change it to be a 2nd or 3rd level spell similar to Magic Mouth, targetable (touch) on your familiar but doesn't need to be "pre-loaded" like a normal Magic Mouth. You can already listen through a familiar, range is unclear but implied 100'. Or, the familiar can cast a touch spell, say normal Magic Mouth that would be loaded at time of casting, technically the familiar spellcasting requires touching a creature but IMHO it would be close enough. That definitely suffers the 100' distance, so preloading the spell might be a closer-to-normal way to do it.
The 2 spells for comparison:
Faithful Companion
Smaller creature is summoned (monkey, parrot, dog, etc.), follows simple orders (fetch, guard, attack)
Find Familiar
1st‐level conjuration (ritual)
You gain the service of a familiar, a spirit that takes an animal form you choose. [statistics and rules removed]
1. within 100 feet of your familiar, you can communicate with it telepathically.
2. as an action, you can see and hear through your familiar's senses
3. your familiar can deliver a spell that requires touching a creature.