Do I need to file a form 8886 for reportable transactions if my losses as a partner on those transactions are less than $7k?

Who Must File - note that there are various categories of listed transactions and some have exceptions for reporting (example section 165 loss transaction) . if the exception is met the transaction is not a listed transaction 

Any taxpayer, including an individual, trust, estate, partnership, S corporation, or other corporation, that participates in a reportable transaction and is required to file a federal tax return or information return must file Form 8886 - no $ limit is specified

Exceptions to Reportable Transaction Categories,

Published Guidance

A transaction is not considered a reportable transaction if the IRS makes a determination in published guidance that it is not subject to the reporting requirements. For more information, see Rev. Proc. 2004-66; Rev. Proc.2004-67, 2004-50 I.R.B. 967, available at IRS.gov/pub/irs-irbs/irb04-50.pdf; Rev. Proc. 2004-68; and Rev. Proc. 2007-20. The IRS  may also determine by individual letter ruling that an individual letter ruling request satisfies the reporting requirements. 

check to see which category is applicable and if there is an exception for reporting 

https://www.irs.gov/pub/irs-pdf/i8886.pdf