Is your expectation that soil salinity has some distinctive signature you will be able to extract directly from the image's bands? Perhaps a more detailed description of your methodology will yield a helpful answer - especially if you provide some citations / references for your analysis.
All you mention is 'Landsat', - so there is probably over 8 million scenes over a span of fifty years, with several major changes in resolution and number of bands and their wavelengths. Those scenes cover about 510 million square kilometers of land area ranging from arctic tundra to equatorial desert. And the term 'soil salinity' is generic if one considers the sources, influencing processes, and resulting conditions. What you are asking with the information you provide is the equivalent of 'how do I find trees in a Landsat image' - without any context, any answer will be partly or all wrong ( trees in the Eastern US turn colors in fall and then lose their leaves, for instance, so some types of NDVI don't work ). Take a guess at how many different ways there are to calculate an NDSI indices? 'Doesn't work' gives no description of exactly what it is that is not working ( the 'tool chain') - there is a practically infinite number of reasons that could be the cause, from not having your computer turned on to using integer versus floating point math.
The quality of any response is going to be directly proportional to the specificity and effort put into the question.
( and Google Scholar is your friend: https://scholar.google.com/scholar?hl=en&as_sdt=0%252C48&q=NDSI+salinity+index
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