How to style a LineString feature to be red colored?

You cannot just set a style as feature property and expect it to work. If you set properties in the constructor, they will be feature properties. You can either use setStyle() on the feature after the feature is constructed:

var myFeature = new ol.Feature({
  geometry: myGeometry,
});
myFeature.setStyle(myStyle);

or you can configure the vector layer with a style function that picks the style attribute from the feature:

new ol.layer.Vector({
  style: function(feature, resolution) {
    return feature.get('style');
  }
})

Instead of "red" in your stroke line, use the RGB value of red: 255,0,0

var myFeature = new ol.Feature({
   geometry : new ol.geom.LineString(coordinates),
   style : new ol.style.Style({
       stroke : new ol.style.Stroke({color : 255,0,0
    })
   })
 });
mySource.addFeature(myFeature);