This will not completely answer your question but my daughter creates mindmaps using Dia and I use LaTex (although not Kile), I use MikTex and LiveTex.
The common denominator is that both have XML and SVG compatibility. You may have to do some additional research about integration capability as I have never come across your integration requirement before.
Before I continue with my answer, if you don't know already, there is a dedicated TeX/LaTeX Q&A in Stack Exchange. It might not do any harm asking your question there also. Lets start with mind mapping and Dia
Dia is available from the Ubuntu Software Centre and is inspired by Microsoft 'Visio,' though more geared towards casual and informal diagrams including Mind Maps. It can be used to draw many different kinds of diagrams with "special objects" to help draw entity relationship diagrams, UML diagrams, flowcharts, network diagrams, and many other types. My daughter swears by this application (if that’s worth anything)
It can load and save diagrams to a custom XML format (a format also supported in LaTex), as well as exporting diagrams to a number of formats, including EPS, SVG, XFIG, WMF and PNG, and can print diagrams (including ones that span multiple pages). You may want to refer a question asked here "How to convert latex equations to SVG" as I think this will be an integral step in your final solution.
You can also create custom shapes for Dia Or download additional shapes from their repository here.
I think your requirement(mindmapper +mathematics+LaTeX) begs more clarity regarding what your expectation is, you give an example of LaTeX (using ie) but it would be very useful if we could undertstand your objective better.