I serve on the scientific advisory board of a private company; can my honorarium listed as a royalty on my 1099-MISC be declared qualified business income?

No, since I assume the royalty is going on a Schedule E. The Qualified Business Income Deduction applies to:

This new deduction applies to Schedule C filers (sole proprietorships and other self-employed businesses), LLCs, partnerships, S corporations, estates, and trusts. Certain rental enterprises may also qualify. Corporations are not eligible because they received their own tax breaks under the TCJA.

If you have other questions about this, ask in the comment section below.

This is a complicated issue. Here is a great FAQ that explains it all:

https://ttlc.intuit.com/replies/7019998

Why hasn't everyone discovered that 1099MISC or 1099 anything have been deemed by the Tax Court of Appeals as "insufficient evidence" on its own to establish a taxpayer's income?  Why do you think there IRS provides a form 1099c (c represents the correction to an issued 1099 from a source) to correct this mistake by the issuer of the 1099.  As evidence of these statements I provide the following  court citations:

Estate of Gryder v. Commissioner,

T.C. Memo. 1993141,

1993 WL 97427,  T.C.M. (CCH)2298,

Portillo v. commissioner, 988 F.2d 27, 29 (th Cir. 1993)  stated a Form 1099 is insuficient to form a rational foundation for the tax assessment against the taxpayers in this case.  Thus, while a Form 1099 can serve as the basis for the inception of an IRS investigation, it cannot and does not, on its own, create tax liability or establish how much income the taxpayer actually received."

Daines v. Alcatel, S.A. 10 F. Supp 2d 113, 113 E.D. Washington, 2000

A declaration of Wages on a W-2 doesn't represent a fact unless it can be shown the wages received resulted from performing action dictating a tax liability.  Now you ask, what creates a tax liabilty?  The answer is stated in "The 78 Congressional Record of 1943, Vol. 2, page 2580 (3rd column to the right) it's the exercise of a excise tax or the job performance based upon a privilege. "   Look at Title 26 USC Section 3402(p) too,  it requires receiving a payment from a Federal Source.....(read it yourselves and be enlightened by making your paychecks great again).  But knowing this doesn't help unless you know which forms to use to correct the lies given to you on your 1099, or  W2 and correctly filling out your W-4 with your Employer. Read the instruction booklet for the W-4 and search for the "EXEMPT" information and following instructions on where to place that word "EXEMPT".  Another helpful hint is to look at form 4852.  What is the title to this form?  Then ask why is the IRS providing such a form? Because, they know the difference between income from Federal sources and Private Enterprises ( WalMart, Boeing, L&M, BestBuy, etc ) while we didn't.  Therefore by exclusion Private Enterprise paychecks  do not create a tax liability.  Stop accepting lies from others, bearing false witness against yourself, and be the authoritative figure in knowing whether you get a Federal sourced paycheck or one from Private Companies (even Mom and Pop stores).  And if IRS challenges you, challenge them back (because your dealing with an ignorant employee acting as a domestic terrorist as described in Title 18 USC  section 2331 (b)(I)(II) who needs to be called out and prosecuted. But they may be challenging you because you did something wrong and contradictory to your new intentions. For your information Statutory references are not arguable in Court by even the best attorneys because the Judges accept it as a fact not subject to interpretation from a Silver Tongued lawyer.  

    Grasp the fact, that the IRS can start asking you to show proof of your Federally sourced paycheck, and you have no substantial evidence in your defense to win, which will subject you to a CIVPEN of $5,000 for a Frivolous 1040 return.  I leave you with the question - do you want to tell the truth on your 1040 with substituted W-2 form using form 4852 and (1099c when needed) or will you continue to accept tax liabilities placed upon you by ignorant employers and payers, ultimately exposing you to a Frivolous return CIVPEN of $5,000 which in turn robs you of your hard earned payments from services rendered?  The choice is yours, and you will have to ultimately bear the consequences.  At least be on the correct side of the Statutory Tax Law, no matter how strange it may sound from what you grew up with.  The Law is the written Law and not the "hear say" you heard from you Uncle Joe or Auntie Jane.