I want to upload a SVG document with a CC BY-SA 3.0 license to an online wiki with a CC BY-NC-SA 3.0 license.
Will these licenses conflict with each other, or can they coexist?
As curiousdannii said licenses do not apply to the original author since they are defining the terms of the re-use of the creations. The author always able to release (or re-release) his/her own work using any license, or no license, or no permissions at all. (But when something is released under a non-revokable license then the author have no way to forbid the usage within the said license terms, but have the right to release it again under a different, more or less restrictive license.)
Other aspect is when there is a document licensed using License-A (by its original author who is not you) and you want to use it in a project using License-B. There is two sides of the story:
This is generally true when it's a collection, like a package of otherwise intact and separate works: the whole collection does have a license but its parts may have more liberal ones. The collection isn't allowed to restrict the more liberal licensing of its part but may utilise its restrictive license to the collection as a whole.
(Wikipedia does the opposite, which is also possible, but much harder to ensure: they include some more restrictive licensed works and explicitly and visibly state that their license is different from the collection's. This is legal but it's very hard to ensure that for every possible way of use the end-user is properly informed about the restrictions.)