How can I use an align environment flush left?

As Andrew mentions you can use \usepackage[fleqn]{amsmath}, but this will mean tha all you equations will be moved to the left.

However, if you want to be able to have some centered and some on the left, then you can use the flalign environment. But, note the trailing & that is required when this is used. As mentioned by egreg, the trailing & in the flalign environment is only required in one of the lines.

\documentclass{article}
\usepackage{amsmath}% mathtools includes this so this is optional
\usepackage{mathtools}

\begin{document}
\begin{align*}% centered
\cos\theta_1 \cos\theta_2-\sin\theta_1\sin\theta_2 &= \cos(\theta_1 +\theta_2) \\
\sin\theta_1 \cos\theta_2 + \cos\theta_1 \sin\theta_2 &= \sin(\theta_1+\theta_2)
\end{align*}

\begin{flalign*}% left aligned
\cos\theta_1 \cos\theta_2-\sin\theta_1\sin\theta_2 &= \cos(\theta_1 +\theta_2) &\\
\sin\theta_1 \cos\theta_2 + \cos\theta_1 \sin\theta_2 &= \sin(\theta_1+\theta_2) &% Need tailing alignment char to get all the way left
\end{flalign*}
\end{document}

I removed the \; from the OP's MWE, which inserted additional spacing where it was not necessary.

The amsmath package has a fleqn option which, according to the manual (texdoc amsmath) has the following effect:

Position equations at a fixed indent from the left margin rather than centered in the text column.

Thus:

\usepackage[fleqn]{amsmath}

seems to be what you are after.

The mathtools package loads amsmath internally and passes any unknown arguments on to it. This includes the fleqn option. Thus:

\usepackage[fleqn]{mathtools}

also works.

Here's a comparison of the outputs. The upper one is without fleqn and the lower one with.

I'm not sure what you mean by "immitate", but I guess you mean you don't want the equations centered, but aligned in another way. A MWE would have been nice, to better understand your problem, to know what documentclass you are using, etc. Anyway, you can have equations aligned differently with align, if you load the amsmath package and write something like this:

\documentclass[a4paper,10pt,fleqn]{article}
\usepackage{amsmath}
\setlength{\mathindent}{1cm}
\begin{document}
\noindent Blah
\begin{align*}
y = ad + da\\
y = ad + da
\end{align*}
\end{document}

As you probably guessed, \setlength{\mathindent}{1cm} lets you control the indentation.