You should have started in Illustrator if that’s what you need to use. There is no reliable way to go from InDesign to Illustrator.
If it’s a very simple layout you could try to export a PDF and open that in Illy but the results are not likely to be very good with anything complicated.
InDesign CS3 was the last version that could export to SVG.
See this: Re: Indesign and SVG
All versions that are able to work with the Publish Online feature are able to export live text to SVG shapes (outlined text) as part of a Publish Online document. The same should be true for Fixed Layout EPUB. But that's only for live text on a page. Not for graphic frames or graphic lines.
Also worth a try:
Export to EPS and open the EPS with Illustrator.
I thought of SVG Kit as well.
And tried to install the 30-days-trial with my InDesign CS6 v8.1.0 (German) on Mac OSX 10.6.8 (German)
After running through the installation process the installer said all is well, but I could not find SVG Kit's functionality after starting InDesign. Strange…
I noticed that the SVG-for-Adobe-2.0-x86-setup.dmg I downloaded is about 42 MB in size wheras the installation notes on the Scand Ltd website tell that the installer should be about 175 MB: Download Trial . Maybe its only a setup package (SVG-for-Adobe-2.0.pkg) that should load the full installer, but obviously that did not happen in my case.
Note: For newer versions of InDesign, up to InDesign CC 2015, the installer is only available for the Windows version of InDesign. Latest version of the installer is from 10 Sep, 2015. InDesign CC 2015.1 was issued August 11 2015, CC 2015.2 November 30, 2015. So I assume SVG Kit should be compatible at least with InDesign CC 2015.1. Not with CC 2017.
Maybe I will try another installation of SVG Kit on OSX 10.7.5 and CS6 later.