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I have several \message commands for inserting information into the log file, and they use ^^J for inserting line breaks in the log file. After adding \usepackage{breqn}, the log file now contains ^^J instead of line breaks. The breqn documentation says the ^^J is affected, but it doesn't say what to do in order to replace the functionality of ^^J in \message command arguments.

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This happens as breqn makes ^ a plain character rather than the superscript char. The low-level TeX convention that (for example) ^^J is a newline is based on having two superscript chars in a row, so this no longer works. You can save a definition in which you have the right type of ^

\documentclass{article}
\newcommand\MBreak{^^J}
\usepackage{breqn}

\begin{document}

\message{Hello\MBreak World}

\end{document}

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