I'm not sure if it's out for the Z Flip 3 yet.
If it is and you don't see the invite in the notices section on the Members App
Then it's likely that your phone was bought through a carrier network and it won't be eligible
The beta program is for unlocked phones only.
So if you bought your phone through a network provider, it will have carrier specific software for network optimisations etc.
Even if you can use other sim cards in the phone, it still has a network lock