No.

The chances are almost nill.

Admission to private colleges is subject to the number of seats available in that particular college and also the amount of fee to be paid.

Generally, the cutoff for BAMS/BHMS remains lower than MBBS/BDS.

Also, the private college cutoff is most variable type. As the colleges with low fees tend to have higher cutoff and high fees colleges have low cutoff.

Cutoff for general category remains 300+ and for OBC category remains 280+.

All the best.

Hey brother, you seem to just qualify the eligibility criteria for neet. But getting a BAMS college is way difficult at this marks. Kindly mention the state you stay in since depending upon your state you may have chances. You can try under management quota seats since you might surely get a seat through it but the fees will be very high so try only if you can afford those fees. 

Thank you.