Video downloader app implemented in RxJs
Overall, I think this is very decent code, some observations:

JSHint


Use JsHint ;)
You have a number of missing semicolons, and an unnecessary semicolon
return url = new Buffer(url, 'base64').toString('ascii'); &lt;- I dont think you wanted to assign to buffer?
You are not using the function fileName(url, season, episode){ anywhere


Odd stuff


You use the extremely cool fetchContent({ url }); but also the mundane 

{
  response: response,
  body: body,
  args: args
}


You should stick to 1 approach
Your regex /"http(.*)(\.flv|\.mkv|\.mp4)"/ 


Is not supporting avi, wmv, or mpg file extensions. 
Is not supporting uppercase incoming file names extentions.
Keeps repeating the \. for each extension, so I would keep that out of the brackets.
If you plan for many entries, then I would keep the regex outside of the function, and generate that regex only 1 single time for performance

You have a stray console.log(params.url);, get rid of it
It seemed odd that the HTML you prepare has no text in the anchor:

return `&lt;a href=${url}&gt;&lt;/a&gt;`;


Also, do you want to consider at least surrounding the URL with double quotes?  


Sugar


You use req.body 3 times in getResult, I would have had a var params = req.body; as a shortcut 
This seems a good use case for a ternary:

if (matches &amp;&amp; matches[0]) {
    return 
} else {
    return null;
}


could be 

return (matches &amp;&amp; matches[0]) ? matches[0] : null;     


I am still not sure why you return null actually. PrepareHtml will return &lt;a href=null&gt;&lt;/a&gt;, so perhaps consider

return (matches &amp;&amp; matches[0]) ? matches[0] : '';     



Anonymous functions kill kittens every day


The 3 functions within your subscribe call are anonymous. It is in general terrible to look at a stack trace filled with anonymous functions
You also have one in getEpisodeRange
I do like that you declare your other functions 'the right way'


Comments go a long way


getEpisodeRange needs comments, it is the most intense code
There are actually no comments at all in this code, and I can parse everything just fine except the above mentioned function 


Style


Formatting looks good to me
Naming looks good to me
I did not find obvious repetitions from a DRY perspective