\flushleft with p{} option in tabular

Load the array package and write

\begin{tabular}{>{\raggedright}p{.3\textwidth}
                >{\raggedright\arraybackslash}p{.6\textwidth}}

It's necessary to use the \arraybackslash in the last column, otherwise \\ would not end the table row. You can use \newline to end lines in the last column cells (and the regular \\ in the other column cells).

By the way, a tabular specification like yours will give an overfull box, as you are not keeping into account the intercolumn spaces. If you want that the table extends all the way of the line width, say

\begin{tabular}{@{}>{\raggedright}p{.3\textwidth-\tabcolsep}
                >{\raggedright\arraybackslash}p{.7\textwidth-\tabcolsep}@{}}

after loading the calc package. Or, without it

\begin{tabular}{@{}
                >{\raggedright}
                p{\dimexpr.3\textwidth-\tabcolsep\relax}
                >{\raggedright\arraybackslash}
                p{\dimexpr.7\textwidth-\tabcolsep\relax}@{}}

The two @{} avoid the insertion of the intercolumn space before and after the tabular.

You could use a feature of the array package to insert a \raggedright command for flush left text, use >{command} before the column definition to insert one or several command(s):

\documentclass{article}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{array}
\begin{document}
\begin{tabular}{>{\raggedright\arraybackslash}p{.3\textwidth}p{.7\textwidth}}
    \blindtext & \blindtext
  \end{tabular}
\end{document}

You mentioned \flushleft - you could use it but it can insert undesired vertical space, such as

\begin{tabular}{>{\flushleft\arraybackslash}p{.3\textwidth}<{\endflushleft}p{.7\textwidth}}

If you need it often, consider defining a new column type using array features, as I did here:

\newcolumntype{P}[1]{>{\raggedright\arraybackslash}p{#1}}

Some people define further useful types, such as

\newcolumntype{C}[1]{>{\centering\arraybackslash}p{#1}}

etc. So your tabular definition becomes simpler:

\begin{tabular}{P{.7\textwidth}P{.3\textwidth}}

In narrow columns, it may be good to allow hyphenation. This can be done using ragged2e. microtype could improve even more. So I would use:

\documentclass{article}
\usepackage[english]{babel}
\usepackage{blindtext}
\usepackage{array}
\usepackage{ragged2e}
\usepackage{microtype}
\newcolumntype{P}[1]{>{\RaggedRight\hspace{0pt}}p{#1}}
\begin{document}
\begin{tabular}{P{.7\textwidth}P{.3\textwidth}}
    \blindtext & \blindtext \\
  \end{tabular}
\end{document}

With ragged2e commands \arraybackslash is not needed. As the first word in a box would not be hyphenated, I additionally inserted zero horizontal space.