OmniGraffle is not available for Linux but there are plenty of alternatives that runs on Linux with similar functionality. The best Linux alternative is diagrams.net, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 50 alternatives to OmniGraffle and many of them are available for Linux so hopefully you can find a suitable replacement. Other interesting Linux alternatives to OmniGraffle are Pencil Project (Free, Open Source), yEd Graph Editor (Free), LibreOffice - Draw (Free, Open Source) and Dia (Free, Open Source).
diagrams.net (previously draw.io) is a free online diagram drawing application for workflow, BPM, org charts, UML, ER, network diagrams. No login or registration are required and features include the ability to save locally (including SVG), a range of stencils, .
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Most users think diagrams.net is a great alternative to OmniGraffle.
Draw lets you produce anything from a quick sketch to a complex plan, and gives you the means to communicate with graphics and diagrams. With a maximum page size of 300cm by 300cm, Draw is a an excellent package for producing technical drawings, general posters, and much else.
PlantUML is an open-source tool that uses simple textual descriptions to draw UML diagrams. The generator can be run anywhere within JVM and integrated with various application such as wiki, text editor, IDE, programming language, documentation generator, and others.
Graphviz is open source graph visualization software. It has several main graph layout programs. It also has web and interactive graphical interfaces, and auxiliary tools, libraries, and language bindings.