Here is the method I implemented to get the file to share. I seem to be having an issue with sharing the image to Google+ but everything else (I tested Dropbox, Twitter, Gmail, and Instagram) worked fine.
private void doSendIntent(String fileName) {
Intent sendIntent = new Intent(android.content.Intent.ACTION_SEND);
sendIntent.setType("image/png");
sendIntent.putExtra(android.content.Intent.EXTRA_SUBJECT, "Drawsaur");
sendIntent.putExtra(android.content.Intent.EXTRA_TEXT, "Check out my drawing I made with Drawsaur!");
Uri uriFile = Uri.fromFile(new File(fileName));
sendIntent.putExtra(android.content.Intent.EXTRA_STREAM, uriFile);
sendIntent.addFlags(Intent.FLAG_GRANT_READ_URI_PERMISSION);
sendIntent.addFlags(Intent.FLAG_GRANT_WRITE_URI_PERMISSION);
this.cordova.startActivityForResult(this, Intent.createChooser(sendIntent, "Share Drawsaur Image Using"), 0);
}