How to remove all layers and features from map?

Loop over all the layers added to the map using the eachLayer method of L.Map, then call the removeLayer method of L.Map on each of them:

map.eachLayer(function (layer) {
    map.removeLayer(layer);
});

References:

eachLayer: http://leafletjs.com/reference.html#map-eachlayer

removeLayer: http://leafletjs.com/reference.html#map-removelayer

Please note that this wil remove ALL the layers from your map. That means also any tilelayers etc. I think in your case it would be best if you do not add all your featureLayers to the map instance, but create a group for them:

// Create group for your layers and add it to the map
var layerGroup = L.layerGroup().addTo(map);

$.getJSON('distributor-companies', function (data) {

    $.each(data, function (i, item) {
        if (item.geojson != '') {
            // Add the new featureLayer to the layerGroup
            var featureLayer = L.mapbox.featureLayer().addTo(layerGroup);
            $.getJSON('/geojson/' + item.geojson, function (data) {
                featureLayer.setGeoJSON(data);
                featureLayer.eachLayer(function (layer) {
                    layer.on('click', function (e) {
                        map.fitBounds(featureLayer.getBounds());
                    });
                });
            });
        }
    });
});

Now you can call the clearLayers method of L.LayerGroup which will clear of the current layers in the group:

layerGroup.clearLayers();

Reference:

L.LayerGroup: http://leafletjs.com/reference.html#layergroup

clearLayers: http://leafletjs.com/reference.html#layergroup-clearlayers

You can use the following truthy check to see if it's a valid geoJSON object:

map.eachLayer(function(layer) {
  if (!!layer.toGeoJSON) {
    map.removeLayer(layer);
  }
});