Credit card rewards are treated as rebates and are not taxable, thus will not be reported on the 1099. While the rewards on the credit card would not be treated as income at time of payment, fluctuations in value may have potential tax implications.
Once rewards are paid out on the credit card, BlockFi will track the cost basis for you. Any future trading activity you conduct that includes the credit card rewards received may generate capital gains/losses that may be taxable and included on the 1099.
We recommend you consult with your tax advisor with any questions for the tax implications related to credit card rewards.