Monks can use daggers as monk weapons, that part makes sense and is clear. Also, a character can dual wield daggers and thrown them both if they use action + bonus action.
But as daggers benefits from the specific martial arts bonus rule (You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.) Does that mean the monk will get bonuses to both attacks just as if they were to attack with 2 different unarmed strikes? Important to remember that the book states Specific Beats General as stated:
This book contains rules, especially in parts 2 and 3, that govern how the game plays. That said, many racial traits, class features, spells, magic items, monster abilities,
and other game elements break the general rules in some way, creating an exception to how the rest of the game works. Remember this: If a specific rule contradicts a general rule, the specific rule wins.
Best Answer
No, the 2nd attack won't get a bonus to damage.
The Monk's Martial Arts feature says:
So, in effect, this allows you to switch Strength bonuses to attack and damage rolls to being Dexterity bonuses to attack and damage rolls. However, the two weapon fighting rule says:
So when using two weapon fighting, you don't have a bonus to your damage roll. If there was one, and it was Strength, Martial Arts would allow you to change it into Dexterity. But Martial Arts doesn't let you create a bonus to damage that doesn't already exist.