Real world solution: make a guess or use your income. All you're looking for is the tax rate.
Official answer: From the instructions for form 8615:
Parent's return information unavailable. If a child can’t get the
required information about their parent's tax return, the child (or the
child's legal representative) can request the necessary information
from the IRS.
How to request. After the end of the tax year, send a signed,
written request for the information to the Internal Revenue Service
Center where the parent's return will be filed. (The IRS can’t process
a request received before the end of the tax year.)
The request must contain all of the following.
• A statement that you are making the request to comply with
section 1(g) of the Internal Revenue Code and that you have
tried to get the information from the parent.
• Proof of the child's age (for example, a copy of the child's birth
certificate).
• Evidence the child has more than $2,600 of unearned income
(for example, a copy of the child's prior year tax return or copies
of Forms 1099 for the current year).
• The name, address, social security number (SSN) (if known),
and filing status (if known) of the parent whose information is to
be shown on Form 8615.
A child's legal representative making the request should include a
copy of their Power of Attorney, such as Form 2848, or proof of legal
guardianship.
If the parents' taxable income, filing status, or net unearned income
of the parents' other children isn't known by the original due date of
the child's return, the child should request an extension of time to file
using Form 4868, Application for Automatic Extension of Time To
File U.S. Individual Income Tax Return.
https://www.irs.gov/pub/irs-pdf/i8615.pdf
