Yes, it is possible to be saved and walk after the flesh.
Then the Promises have not happened to you as of yet . . .
If "you" are walking in the flesh, meaning that a person is living in and by the Sinful Nature, then God has not performed His Holy Operation of Faith upon "your" unregenerate heart.
Ezekiel 36:25-27 KJV - "Then will I sprinkle clean water upon you, and ye shall be clean: from all your filthiness, and from all your idols, will I cleanse you. A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh. And I will put my spirit within you, and cause you to walk in my statutes, and ye shall keep my judgments, and do them."
Jesus Christ is a fulfillment of this prophecy. . . for Jesus is the only one who Cuts out and Removes the Sinful Nature. It is as clear as a bell, for this is the Purpose of the Bible . . . to Redeem.
Colossians 2:11-12, 14-15 KJV - "In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead. Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross; And having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it."
Whoever has not received the Circumcision of Christ, their Father remains to be the Devil. The Bible affords no alternative.