Income on a Schedule K-1 (Form 1065) from a partnership is only income from self-employment to the extent that it's reported with code A in box 14. Check the Keogh, SEP and SIMPLE Contribution Worksheet to see the calculation of the amount of the self-employed retirement deduction. See that this amount propagates to Schedule 1 line 15.
Also, if income tax is already zero without the 401(k) contribution, the deduction for a self-employed retirement contribution will not reduce your tax liability. The deduction for a self-employed retirement contribution will not reduce other taxes such as self-employment tax.
