No you can not
Unarmed strikes are indeed "weapon attacks", and you don't need to hold a weapon to use a Disarm attack. The issue is that Flurry of Blows specifically states that it lets you perform Unarmed Strikes, not just any weapon attack. Disarm as described in the DMG is not an Unarmed Strike, even if you don't hold a weapon; It's a special weapon attack similar to Grapple and Shove, which you also can't do with Flurry of Blows. An Unarmed Strike is a specific type of melee weapon attack that doesn't use weapons.
PHB pg. 78 (emphasis mine):
Flurry of Blows Immediately after you take the Attack action on your turn, you can spend 1 ki point to make two unarmed strikes as a bonus action
PHB pg. 195:
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike [..]. On a hit, an unarmed strike deals bludgeoning damage equal to 1 + your strength modifier.
Just to rephrase this in another way because apparently the point isn’t getting across: All Flurry of Blows allows you to do is make 2 Unarmed Strikes. Unarmed strikes are very specifically attacking with your body to do damage. It’s a specific type of attack, not a generic description. Disarming someone is never an Unarmed Strike regardless of whether or not you hold a weapon, so you can’t do it with the attacks Flurry Of Blows gives you.
For some official-sounding back up for this, SAC doesn't have a QA on this issue exactly (although it's really not ambiguous), but it has this to say about the (somewhat) similar situation with Attacks of Opportunities:
Can an opportunity attack be used to make a grapple or a shove?
Grappling and shoving are special melee attacks that require the Attack action. An opportunity attack is a special reaction. Take the Ready action if you want to attempt a grapple or a shove as a reaction.
PS: Regardless of the RAW, I personally would allow it at my tables because it’s flavourful and not really a concern from a game balance perspective because disarm is a pretty niche option compared to just straightforwardly hitting people.