Yes Bhavishya Purana is Authentic ,
The following Sanskrit verses are taken directly from the Srimad Bhagavatam of Srila Vyasadeva, the original spiritual master, to support that what we are saying is coming from authorised the word of God that Bhavishya Purana is an authorised book written by Srila Vyasadeva.
brahmam padmam vaisnavam ca
saivam laingam sa-garudam naradiyam bhagavatam agneyam skanda-samhnitam bhavisyam brahma-vaivartam markandeyam sa-vamanam varaham matsyam kaurmam ca brahmandakhyam iti tri-sat
These verses taken from Maha Bhagavata Purana (Srimad Bhagavatam 12:7:23-24) list the eighteen major Puranas that were written by Srila Vyasadeva in His own words. Please note that on the fifth line Bhavishya is mentioned as one of these authorised works.
