Capital sigma missing in Euler font

As barbara beeton mentioned in a comment, flexysym and eulervm don't cooperate. A possible workaroung is to use the savesym package: the idea is to load breqn and then rename the conflicting symbols (the whole Greek alphabet and some others) using \savesymbol. Once this is done, eulervm can be safely loaded.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{breqn}
\usepackage{savesym}
\savesymbol{Gamma}
\savesymbol{Delta}
\savesymbol{Theta}
\savesymbol{Lambda}
\savesymbol{Xi}
\savesymbol{Pi}
\savesymbol{Sigma}
\savesymbol{Upsilon}
\savesymbol{Phi}
\savesymbol{Psi}
\savesymbol{Omega}
\savesymbol{alpha}
\savesymbol{beta}
\savesymbol{gamma}
\savesymbol{delta}
\savesymbol{epsilon}
\savesymbol{zeta}
\savesymbol{eta}
\savesymbol{theta}
\savesymbol{iota}
\savesymbol{kappa}
\savesymbol{lambda}
\savesymbol{mu}
\savesymbol{nu}
\savesymbol{xi}
\savesymbol{pi}
\savesymbol{rho}
\savesymbol{sigma}
\savesymbol{tau}
\savesymbol{upsilon}
\savesymbol{phi}
\savesymbol{chi}
\savesymbol{psi}
\savesymbol{omega}
\savesymbol{varepsilon}
\savesymbol{vartheta}
\savesymbol{varpi}
\savesymbol{varphi}
\savesymbol{infty}
\savesymbol{ldotp}
\usepackage{eulervm}

\begin{document}

\[ \Sigma_1\Delta_2 \]

\end{document}

A more definitive solution would be to create a support file in flexysim for eulervm; this doen't seem to be so hard according to the documentation of breqn:

If you find that a particular math font package doesn’t work then please see implementation in flexisym.dtx for how to create a support file—it is easier than one might think. Contributions welcome.

It seems that

\DeclareFlexSymbol{\Gamma}  {Var}{latin}{00}
\DeclareFlexSymbol{\Delta}  {Var}{latin}{01}
\DeclareFlexSymbol{\Theta}  {Var}{latin}{02}
\DeclareFlexSymbol{\Lambda} {Var}{latin}{03}
\DeclareFlexSymbol{\Xi}     {Var}{latin}{04}
\DeclareFlexSymbol{\Pi}     {Var}{latin}{05}
\DeclareFlexSymbol{\Sigma}  {Var}{latin}{06}
\DeclareFlexSymbol{\Upsilon}{Var}{latin}{07}
\DeclareFlexSymbol{\Phi}    {Var}{latin}{08}
\DeclareFlexSymbol{\Psi}    {Var}{latin}{09}
\DeclareFlexSymbol{\Omega}  {Var}{latin}{0A}
\DeclareFlexSymbol{0}{Var}{latin}{30}
\DeclareFlexSymbol{1}{Var}{latin}{31}
\DeclareFlexSymbol{2}{Var}{latin}{32}
\DeclareFlexSymbol{3}{Var}{latin}{33}
\DeclareFlexSymbol{4}{Var}{latin}{34}
\DeclareFlexSymbol{5}{Var}{latin}{35}
\DeclareFlexSymbol{6}{Var}{latin}{36}
\DeclareFlexSymbol{7}{Var}{latin}{37}
\DeclareFlexSymbol{8}{Var}{latin}{38}
\DeclareFlexSymbol{9}{Var}{latin}{39}

after loading breqn is sufficient. Thanks to Gonzalo for providing the clue.