Chris,
   If you would like to have a draw widget symbololgy set that are specific to you and your needs then several files need some edits/creation.
The symbols that are available in the draw widget come from 10 json files that specify the symbols in json format
[install dir]\server\apps\[app#]\jimu.js\dijit\SymbolsInfo.
The json files then contain (minified) symbols:
[{
    "imageData": "iVBORw0KGgoAAAANSUhEUgAAAEAAAABACAYAAACqaXHeAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAEM5JREFUeF7tWglUlFey7m56gabZN6GbpaGRBgOCkmecYwyJJsYzeU8d44tLnERj4uRNjM84ahaj5o0xiQuJuMcVg1EwwQ0UQRTFBQUlKGLiqIwi4gYIskPzvaq/uxEYVEQz58jhnlOnl
    "height": 24,
    "xoffset": 0,
    "yoffset": 0,
    "width": 24,
    "name": "Airplane",
    "contentType": "image/png",
    "type": "esriPMS",
    "angle": 0,
    "url": "http://static.arcgis.com/images/Symbols/Transportation/Airplane.png"
}, {
The imageData above is the Base64 encoded string of the image file (online utility website for that Base64 Decode and Encode - Online )
So you would create a new 11.json file and add symbol code like above in an array (so you will need your images you will be using to be hosted on a web server).
Then in the [install dir]\server\apps\[app#]\jimu.js\dijit\templates\SymbolChooser.html you would add your new 11.json to the list (line 31 below):
<div style="width:320px;">
     <div class="symbol-section point-symbol-section" data-dojo-attach-point="pointSection">
          <table class="symbol-set-table" cellspacing="0">
               <colgroup>
                    <col width="130px"></col>
                    <col width="auto"></col>
               </colgroup>
               <tbody>
                    <tr>
                         <td>
                              <span>${nls.preview}:</span>
                         </td>
                         <td>
                              <div data-dojo-attach-point="pointSymPreview" style="width:100%;"></div>
                         </td>
                    </tr>
                    <tr class="point-sym-class-select-tr">
                         <td colspan="2">
                              <select class="restrict-select-width" data-dojo-attach-point="pointSymClassSelect" data-dojo-type="dijit/form/Select" style="width:100%;height:30px;">
                                    <option value='0' selected="selected">${nls.basic}</option>
                                    <option value='1'>A-Z</option>
                                    <option value='2'>${nls.arrows}</option>
                                    <option value='3'>${nls.business}</option>
                                    <option value='4'>${nls.cartographic}</option>
                                    <option value='5'>${nls.nationalParkService}</option>
                                    <option value='6'>${nls.outdoorRecreation}</option>
                                    <option value='7'>${nls.peoplePlaces}</option>
                                    <option value='8'>${nls.safetyHealth}</option>
                                    <option value='9'>${nls.shapes}</option>
                                    <option value='10'>${nls.transportation}</option>
                                    <option value='11'>my custom symbols</option>
                              </select>
                         </td>
                    </tr>
That's it now you have a custom symbol set in your apps draw widget that you can use.