I have a different problem on Ubuntu 14.04 (1.5.1 autoinstalled from APT repo):
The main window cannot be open, though other things through the tray icon work. The log file in ~/.config/Insync grows to enormous size (4 GB in my case after 1 hour), being filled by these messages:
libpng warning: iCCP: known incorrect sRGB profile
/usr/lib/insync/QtWebEngineProcess: /usr/lib/insync/libdbus-1.so.3: no version information available (required by /usr/lib/insync/libQt5WebEngineCore.so.5)
[17796:17874:0919/125159.554376:ERROR:gles2_cmd_decoder.cc(2603)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_ENUM : BackFramebuffer::Create: <- error from previous GL command
[17796:17874:0919/125159.554419:ERROR:gles2_cmd_decoder.cc(2607)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_ENUM : BackFramebuffer::Create: was unhandled
[17796:17874:0919/125159.554442:ERROR:gles2_cmd_decoder.cc(2607)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_ENUM : BackFramebuffer::Create: was unhandled
[17796:17874:0919/125159.554469:ERROR:gles2_cmd_decoder.cc(2607)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_VALUE : ScopedFramebufferBinder::ctor: was unhandled
[17796:17874:0919/125159.554502:ERROR:gles2_cmd_decoder.cc(2603)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_OPERATION : ScopedFramebufferBinder::dtor: <- error from previous GL command
[17796:17874:0919/125159.554511:ERROR:gles2_cmd_decoder.cc(2607)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_VALUE : ScopedFramebufferBinder::dtor: was unhandled
[17796:17874:0919/125159.554519:ERROR:gles2_cmd_decoder.cc(2607)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_VALUE : ScopedFramebufferBinder::ctor: was unhandled
[17796:17874:0919/125159.554529:ERROR:gles2_cmd_decoder.cc(2603)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_ENUM : ScopedFramebufferBinder::dtor: <- error from previous GL command
[17796:17874:0919/125159.554540:ERROR:gles2_cmd_decoder.cc(2607)] [GroupMarkerNotSet(crbug.com/242999)!:58140A3CA77F0000]GL ERROR :GL_INVALID_VALUE : ScopedFramebufferBinder::dtor: was unhandled
[17796:17874:0919/125159.554549:ERROR:gles2_cmd_decoder.cc(5385)] GLES2DecoderImpl::ResizeOffscreenFramebuffer failed because offscreen FBO was incomplete.
[17796:17874:0919/125159.554829:ERROR:gles2_cmd_decoder.cc(3708)] ContextResult::kFatalFailure: Could not allocate offscreen buffer storage.
This might help:
$ sudo ldconfig -p | grep -i gl.so
libwayland-egl.so.1 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libwayland-egl.so.1
libwayland-egl.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libwayland-egl.so
libvtkftgl.so.5.8 (libc6,x86-64) => /usr/lib/libvtkftgl.so.5.8
libvtkftgl.so (libc6,x86-64) => /usr/lib/libvtkftgl.so
libvgagl.so.1 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libvgagl.so.1
libva-egl.so.1 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libva-egl.so.1
libva-egl.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libva-egl.so
libmrpt-opengl.so.1.0 (libc6,x86-64) => /usr/lib/libmrpt-opengl.so.1.0
libmrpt-opengl.so (libc6,x86-64) => /usr/lib/libmrpt-opengl.so
libfltk_gl.so.1.1 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libfltk_gl.so.1.1
libfltk_gl.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libfltk_gl.so
libcogl.so.15 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libcogl.so.15
libTKOpenGl.so.8 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libTKOpenGl.so.8
libQt5OpenGL.so.5 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libQt5OpenGL.so.5
libQt5OpenGL.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libQt5OpenGL.so
libQtOpenGL.so.4 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libQtOpenGL.so.4
libQtOpenGL.so.4 (libc6) => /usr/lib/i386-linux-gnu/libQtOpenGL.so.4
libQtOpenGL.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libQtOpenGL.so
libGL.so.1 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/mesa/libGL.so.1
libGL.so.1 (libc6) => /usr/lib/i386-linux-gnu/mesa/libGL.so.1
libGL.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libGL.so
libGL.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/mesa/libGL.so
libEGL.so.1 (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/mesa-egl/libEGL.so.1
libEGL.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libEGL.so
libEGL.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/mesa-egl/libEGL.so
libCgGL.so (libc6,x86-64) => /usr/lib/x86_64-linux-gnu/libCgGL.so
$ ldd /usr/lib/insync/insync
linux-vdso.so.1 => (0x00007ffe6637e000)
libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007f2129c88000)
libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007f2129a84000)
libutil.so.1 => /lib/x86_64-linux-gnu/libutil.so.1 (0x00007f2129881000)
libm.so.6 => /lib/x86_64-linux-gnu/libm.so.6 (0x00007f212957b000)
libz.so.1 => /usr/lib/insync/libz.so.1 (0x00007f2129362000)
libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007f2128f99000)
/lib64/ld-linux-x86-64.so.2 (0x00007f2129ea6000)
$ ldd /usr/lib/insync/py
linux-vdso.so.1 => (0x00007fff5dedc000)
libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007f668656b000)
libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007f6686367000)
libutil.so.1 => /lib/x86_64-linux-gnu/libutil.so.1 (0x00007f6686164000)
libm.so.6 => /lib/x86_64-linux-gnu/libm.so.6 (0x00007f6685e5e000)
libz.so.1 => /usr/lib/insync/libz.so.1 (0x00007f6685c45000)
libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007f668587c000)
/lib64/ld-linux-x86-64.so.2 (0x00007f6686789000)
$ ldd /usr/lib/insync/PySide.QtCore.so
linux-vdso.so.1 => (0x00007fff4a1dd000)
libpyside-python2.7.so.1.2 => /usr/lib/x86_64-linux-gnu/libpyside-python2.7.so.1.2 (0x00007efc64d25000)
libpython2.7.so.1.0 => /usr/lib/x86_64-linux-gnu/libpython2.7.so.1.0 (0x00007efc647c1000)
libshiboken-python2.7.so.1.2 => /usr/lib/x86_64-linux-gnu/libshiboken-python2.7.so.1.2 (0x00007efc64595000)
libQtCore.so.4 => /usr/lib/x86_64-linux-gnu/libQtCore.so.4 (0x00007efc640b0000)
libstdc++.so.6 => /usr/lib/x86_64-linux-gnu/libstdc++.so.6 (0x00007efc63d9a000)
libm.so.6 => /lib/x86_64-linux-gnu/libm.so.6 (0x00007efc63a94000)
libgcc_s.so.1 => /lib/x86_64-linux-gnu/libgcc_s.so.1 (0x00007efc6387c000)
libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007efc634b3000)
libpthread.so.0 => /lib/x86_64-linux-gnu/libpthread.so.0 (0x00007efc63295000)
libz.so.1 => /lib/x86_64-linux-gnu/libz.so.1 (0x00007efc6307c000)
libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007efc62e78000)
libutil.so.1 => /lib/x86_64-linux-gnu/libutil.so.1 (0x00007efc62c75000)
libglib-2.0.so.0 => /lib/x86_64-linux-gnu/libglib-2.0.so.0 (0x00007efc6296d000)
librt.so.1 => /lib/x86_64-linux-gnu/librt.so.1 (0x00007efc62765000)
/lib64/ld-linux-x86-64.so.2 (0x00007efc653f9000)
libpcre.so.3 => /lib/x86_64-linux-gnu/libpcre.so.3 (0x00007efc624f6000)