Ok, another answer, I just realized, these are two slightly different questions - one by the question starter and one by the bounty starter.

I would need a solution to this issue as well. Here is my minimum example expected to work:

---
title: "Testing LaTeX packages in Docx format" 
output: word_document 
header-includes:
  - \usepackage{xfrac} 
--- 
  $$ \sfrac{1}{2} $$ ```

In this case the outlined answer with MathJax will not work so well. sfrac is not supported by MathJax (http://docs.mathjax.org/en/latest/input/tex/macros/index.html)

I don't know if you need \sfrac specifically, but \frac or \tfrac would be supported. Maybe you can use these instead.

Here an example with \frac

 ---
 title: "Frac Test"
 header-includes: 
  - \usepackage{xfrac}
 output:
  pdf_document: default
  html_document: default
  word_document: default
---

$$
   \frac{1}{2}+1
$$

Output of \frac example html:

This will work for .pdf / word and html.

Here an example with \tfrac

---
title: "TFrac Test"
header-includes: 
 - \usepackage{xfrac}
output:
  pdf_document: default
  html_document: default
  word_document: default
---

$$
   \tfrac{1}{2}+1
$$

Output \tfrac example html:

This will run for html, pdf - for word it will write 1/2 instead of a formula, since there is no \tfrac equivalent in word.

\cfrac and \dfrac are also supported by MathJax.

You can somehow solve this for most of the important symbols/characters via Mathjax. Here is a list of supported symbols/characters:http://docs.mathjax.org/en/latest/input/tex/macros/index.html Just look there for the symbol you need.

Then you use it like this:

$$
\require{mhchem}
\begin{equation}
  [C] + [R] 
  \xrightleftharpoons[k_{-1}]{k_1}
  [CR] + [C] 
  \xrightleftharpoons[k_{-2}]{k_2}
  [C2R]
(\#eq:multiplebinding)
\end{equation}
$$

So you need to enclose your command in $$. In this example \xrightleftharpoons was used. From the table I linked you above you can see that you need to add \require{mhchem} in this case. For your case this isn't needed, you just need to write \mathbb.

Example:

  ---
title: "TinyTeX Test"
header-includes:
  - \usepackage{mathbbol}
output:
  pdf_document: default
  html_document: default
  word_document: default
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

Hello Mori, this should work


$$
    \mathbb{1}_{S}(x)
$$

Greetings, Steffen

HTML OUTPUT:

WORD OUTPUT:

Also note, that I replaced bbm with \usepackage{mathbbol} - otherwise it had errors rendering the pdf for me. Here a discussion about bbm on tex.stackexchange ... most people advise against using bbm, since there are better packages to get the symbols https://tex.stackexchange.com/questions/26637/how-do-you-get-mathbb1-to-work-characteristic-function-of-a-set

Ok, so after Steffen's answers, I've come to the conclusion that the proper answer would be: Including LaTeX packages in docx documents cannot be done (at least up to now).

The only solution is to use the equivalent MathJax-supported command/symbol. Nevertheless, Steffen's answer pointed me in the correct direction of the commands supported by MathJax (many thanks!), so I awarded him the bounty.

Also, as my specific problem was with diagonal fractions, I tried all the frac variants allegedly supported by MathJax. There are six of them, out of which the following worked: \dfrac, \frac, and \dfrac, and the following did not: \cfrac, \flatfrac, and \genfrac.