How can I use \not with more than one symbol?

You can use \mathclap from mathtools:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\DeclareMathOperator{\lecolon}{<:}

\begin{document}
\[ \not\mathclap\lecolon \]
%your whole expression should be something like
\[ \gamma\not\mathclap\lecolon\mkern10mu\tau \]
\end{document}

Anyways, I think your expression looks more like the \not reffers only to the less sign and it's followed by a colon:

\[ \gamma\not\mathclap<:\tau \]

which can finally be slightly refined to

\[ \gamma\mkern-2mu\not\mkern2mu\mathclap<:\tau \]

Here my MWE. What do you prefer?

\documentclass[a4paper]{article}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}
%%%%%%%%%%%%%%%%%%%%%%%%Useful packages
\usepackage{amsmath}
\usepackage{centernot,cancel}

\begin{document}

\[
  \cancel{<:} ~~~~\text{or}~~~~ \centernot{<:}
\]

\end{document}

Choose a more representative name of what you are talking about with that symbol. Note that the standard is to use \n<relation name> to show the negated symbol of \<relation name>, so you may want to adhere to that.

\documentclass{scrartcl}

\usepackage{centernot,amssymb,mathtools}

\newcommand*\somekindofrelation{\mathrel{<:}}
\newcommand*\nsomekindofrelation{\mathrel{\centernot{<}\vcentcolon}}

\begin{document}

\[ \gamma \nsomekindofrelation \tau \]

\end{document}

EDIT Result: