As biblatex does not distinguish multiple first names, we need to split this list ourselves:
\makeatletter
\def\@empty{}
\def\first#1{\expandafter\@first#1 \@nil}
\def\@first#1 #2\@nil{#1\addspace%
\if\relax\detokenize{#2}\relax\else\@initials#2\@nil\fi}
\def\initials#1{\expandafter\@initials#1 \@nil}
\def\@initials#1 #2\@nil{%
\initial{#1}%
\def\NextName{#2}%
\ifx\@empty\NextName\relax%
\else\@initials#2\@nil\fi}
\def\initial#1{\expandafter\@initial#1\@nil}
\def\@initial#1#2\@nil{#1.\addspace}
\makeatother
Now calling \first{John Arthur Kyle} yields "John A. K.".
The trick used is that the macro \first passes its argument to \@first which in turn delimits its arguments by spaces, i.e. #1 is "John" and #2 is "Arthur Kyle". This gets sent to \@initials which goes through the list of names (in case there are more or less than two) and calls \initial with each name. \initial in turn calls \@initial which throws away all but the first letter and adds a dot and a space.
Now we can use this in \DeclareNameFormat:
\def\bibnamedelima{ }%
\def\bibnamedelimb{ }%
\DeclareNameFormat{author}{%
\ifblank{#5}{}{#5\addspace}% prefix if applicable
#1% last name
\edef\firstname{#3}%
\ifblank{#3}{}{\addcomma\addspace\expandafter\first{\firstname}}%
\ifthenelse{\value{listcount}<\value{liststop}}%
{\addslash}{}%
}
Note that for author = {Doe, John Arthur Kyle} in the bib file, #3 actually consists of John\bibnamedelimb Arthur\bibnamedelima Kyle, so we need to eliminate these for the \first macro to work.
EDIT: a "proper" NameFormat should include deliminators for multiple names, thus we check if we are in the middle of a list of names and if so print a slash.
Additionally, the authoryear style uses labelname to display the author name in citations, so that format should be changed to keep the formatting of the citation in line with that of the bibliography entry:
\DeclareNameFormat{labelname}{%
\ifblank{#5}{}{#5\addspace}% prefix if applicable
#1% last name
\edef\firstname{#3}%
\ifblank{#3}{}{\addcomma\addspace\expandafter\first{\firstname}}%
\ifthenelse{\value{listcount}<\value{liststop}}%
{\addslash}{}%
}
To summarize: This code
\documentclass{scrartcl}
\usepackage[backend=biber,style=authoryear]{biblatex}
\bibliography{bibliography}
\usepackage[T1]{fontenc}
\def\bibnamedelima{ }%
\def\bibnamedelimb{ }%
\DeclareNameFormat{author}{%
\ifblank{#5}{}{#5\addspace}% prefix if applicable
#1% last name
\edef\firstname{#3}%
\ifblank{#3}{}{\addcomma\addspace\expandafter\first{\firstname}}%
\ifthenelse{\value{listcount}<\value{liststop}}%
{\addslash}{}%
}
\DeclareNameFormat{labelname}{%
\ifblank{#5}{}{#5\addspace}% prefix if applicable
#1% last name
\edef\firstname{#3}%
\ifblank{#3}{}{\addcomma\addspace\expandafter\first{\firstname}}%
\ifthenelse{\value{listcount}<\value{liststop}}%
{\addslash}{}%
}
\makeatletter
\def\@empty{}
\def\first#1{\expandafter\@first#1 \@nil}
\def\@first#1 #2\@nil{#1\addspace%
\if\relax\detokenize{#2}\relax\else\@initials#2\@nil\fi}
\def\initials#1{\expandafter\@initials#1 \@nil}
\def\@initials#1 #2\@nil{%
\initial{#1}%
\def\NextName{#2}%
\ifx\@empty\NextName\relax%
\else\@initials#2\@nil\fi}
\def\initial#1{\expandafter\@initial#1\@nil}
\def\@initial#1#2\@nil{#1.\addspace}
\makeatother
\begin{document}
\cite[123]{Doe}\par
\cite[124]{Doe2}\par
\cite[125]{vD}
\printbibliography
\end{document}
together with this bib file:
@book{Doe,
title = {The secret life of John Doe},
author = {Doe, John Arthur Kyle and Jane Emma Dane and Someone Else},
year = {2013}
}
@book{Doe2,
title = {The secret life of John Doe 2},
author = {Doe, John},
year = {2013}
}
@book{vD,
title = {The secret life of John von Doe},
author = {John Arthur Kyle von Doe},
year = {2013}
}
produces this output:

EDIT: For more details on splitting strings, see e.g. the answers to this question; for information on macros using "strange" argument delimiters, see e.g. this thread.
\DeclareNameFormatseems to be the right way. Even if I ignore middle names, I cannot find a way to 'tokenize' the list of first (and middle) names. Next step would be assign style #3 (first names written out) to the first token (\ifnumequal{1}) and style #4 (first names as initials) to the rest (\ifnumgreater{1}or some kind of 'else' resulting from\DeclareNameFormatsyntax). – G. H. Jul 31 '13 at 12:31