How to typeset vedic fonts/symbols in kannada?

You simply have to use a Kannada font that includes the Vedic accents. According to Sridatta here,

As per Jelle Bosma of Monotype, the designer of Noto Sans Kannada, it should work in the latest Phase III fonts. […] You can get the fonts here https://github.com/googlei18n/noto-fonts/tree/master/phaseIII_only

And indeed, after downloading Noto Sans Kannada from there (e.g. this file), I can get it to work:

\documentclass{article}
\usepackage{fontspec}
\setmainfont[Script=Kannada,Path=$HOME/Downloads/]{NotoSansKannada-Regular.ttf}
\tracinglostchars=2 % https://tex.stackexchange.com/q/41230/48
\begin{document}

ಆ ನೋ᳚ ಭ॒ದ್ರಾಃ ಕ್ರತ॑ವೋ ಯನ್ತು ವಿ॒ಶ್ವತೋಽದ॑ಬ್ಧಾಸೋ॒ ಅಪ॑ರೀತಾಸ ಉ॒ದ್ಭಿದಃ॑ ।
ದೇ॒ವಾ ನೋ॒ ಯಥಾ॒ ಸದ॒ಮಿದ್ ವೃ॒ಧೇ ಅಸ॒ನ್ನಪ್ರಾ᳚ಯುವೋ ರಕ್ಷಿ॒ತಾರೋ᳚ ದಿ॒ವೇದಿ॑ವೇ ॥ 1.089.01

\end{document}

Note that in the same thread, the creator of Goda (and of Bhasha IME) also says it should work with Goda, if your input is valid Unicode. Trying with Goda (get the font here or (not tested) here) works too:

\documentclass{article}
\usepackage{fontspec}
\setmainfont[Script=Kannada,Path=$HOME/Downloads/]{Goda_1_0_6.ttf}
\tracinglostchars=2 % https://tex.stackexchange.com/a/41235/48
\begin{document}

ಆ ನೋ᳚ ಭ॒ದ್ರಾಃ ಕ್ರತ॑ವೋ ಯನ್ತು ವಿ॒ಶ್ವತೋಽದ॑ಬ್ಧಾಸೋ॒ ಅಪ॑ರೀತಾಸ ಉ॒ದ್ಭಿದಃ॑ ।
ದೇ॒ವಾ ನೋ॒ ಯಥಾ॒ ಸದ॒ಮಿದ್ ವೃ॒ಧೇ ಅಸ॒ನ್ನಪ್ರಾ᳚ಯುವೋ ರಕ್ಷಿ॒ತಾರೋ᳚ ದಿ॒ವೇದಿ॑ವೇ ॥ 1.089.01

\end{document}

Similarly with Vagisha_1_0_5.ttf it works too:

If it doesn't work, please check your input for whether it's valid Unicode, and whether the font versions are the same. Also, these were tested with xelatex on macOS; I believe they should also work on Windows (especially 8.1 or later) according to the pages on the font (BhashaIME) site.