Etsy issued a 1099 in my name when it should have been issued to my partnership. Since my portion of income is included in my K-1, can I skip claiming this 1099?

Since the form 1099 was issued under your social security number, you should enter it on your tax return since the IRS will check for it and probably assess tax on it if you don't report it. Just enter an expense for the same amount of money to cancel out the income.