I don’t know if turning off Bluetooth protects against flipper attacks (Edit: Nah.), but unless something has changed, it (sadly) doesn’t preserve your privacy.
It’s not really documented, as far as I can tell, but Bluetooth low energy stays on, even when you toggle Bluetooth off for both iOS and Android. As of iOS 15, even turning off iPhones means the phone is still trackable. (Unsure about Android on that front.) Apple’s ‘Find my’ network uses Bluetooth low energy, same as Bluetooth beacons.