Your flalign does nothing really useful.
Here are two realizations:
\documentclass{article} \usepackage{amsmath} \usepackage{showframe} \begin{document} Really flush left, but requires an odd number of lines to get the equation number centered \begin{flalign} &\text{Level 1:} & y_{ij} &= \beta_{0j} + \beta_{1} x_{ij} + \epsilon_{ij} & \notag\\ &\text{Level 2:} & \beta_{0j} &= \gamma_{00} + \gamma_{01 } z_{j}+ U_{0j} & \label{test} \\ & & \beta_{1j} &= \gamma_{10} & \notag \end{flalign} Not really flush left, adjust manually the dimension to suit your taste (here it is three centimeters) \begin{gather}\label{eq:L1} \begin{alignedat}{2} &\makebox[0pt][r]{\makebox[3cm][l]{Level 1:}} & y_{ij} &= \beta_{0j} + \beta_{1} x_{ij} + \epsilon_{ij} \\ &\makebox[0pt][r]{\makebox[3cm][l]{Level 2:}} & \beta_{0j} &= \gamma_{00} + \gamma_{01 } z_{j}+ U_{0j} \\ & & \beta_{1j} &= \gamma_{10} \end{alignedat} \end{gather} \end{document}
Take your pick. Note: showframe is only used to display the margins of the text block.

The following is what I'd like to see:
\documentclass{article} \usepackage{amsmath} \usepackage{showframe} \begin{document} Not flush left, but probably clearer about your intentions \begin{gather}\label{eq:L1} \begin{alignedat}{2} \makebox[0pt][r]{Level 1:\quad} && y_{ij} &= \beta_{0j} + \beta_{1} x_{ij} + \epsilon_{ij} \\ \makebox[0pt][r]{Level 2:\quad} && \beta_{0j} &= \gamma_{00} + \gamma_{01 } z_{j}+ U_{0j} \\ && \beta_{1j} &= \gamma_{10} \end{alignedat} \end{gather} \end{document}
