You can use the spectral arms to make unarmed strikes.
The Monk's Martial Arts and Flurry of Blows features allow you to use your Bonus Action to make Unarmed Strikes. When you make an Unarmed Strike you may choose to do so with your Arms of the Astral Self. Note the Arms of the Astral Self only interact with Unarmed Strikes and you can't use them to Shove or Grapple an opponent.
Stunning Strike can be used with any Melee Weapon Attack. This includes melee attacks made with Improvised Weapons, Simple Weapons, Martial Weapons, Natural Weapons, and Unarmed Strikes. Basically Stunning Strike can be used with any melee attack that isn't from a spell.
And could they use them for flurry of blows?
Yes, and yes.
From the Arms of the Astral Self feature:
The Monk's Martial Arts and Flurry of Blows features allow you to use your Bonus Action to make Unarmed Strikes. When you make an Unarmed Strike you may choose to do so with your Arms of the Astral Self. Note the Arms of the Astral Self only interact with Unarmed Strikes and you can't use them to Shove or Grapple an opponent.
Stunning Strike can be used with any Melee Weapon Attack. This includes melee attacks made with Improvised Weapons, Simple Weapons, Martial Weapons, Natural Weapons, and Unarmed Strikes. Basically Stunning Strike can be used with any melee attack that isn't from a spell.
Cool! I wanted to make sure because I swear a few years ago it wasn't like that?
A few years (as in 2-4) ago the subclass was only UA
A few years (as in 4-8) the subclass did not exist in any form in 5e.
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Ah, I'm thinking of the UA