How to position elements to the right in md-toolbar?

Or you can use a class for that:

.fill-space {
  // This fills the remaining space, by using flexbox.
  // Every toolbar row uses a flexbox row layout.
  flex: 1 1 auto;
}

<md-toolbar color="primary">
  <span>Application Title</span>

  <!-- This fills the remaining space of the current row -->
  <span class="fill-space"></span>

  <span>Right Aligned Text</span>
</md-toolbar>

This solution is also taken from a spec.

THIS SOLUTION IS FOR ANGULAR MATERIAL v1.X, IF YOU NEED AN UNIVERSAL/ANGULAR MATERIAL v2 SOLUTION CHECK @experimenter ANSWER

If you have a md-toolbar the easiest way to align right content is like this:

    <md-toolbar>
        <div class="md-toolbar-tools">
            <h3>You text</h3>
            <span flex></span>
            <ANY>your right content</ANY>
        </div>
    </md-toolbar>

The flex property in span will cover the space between the contents. This is the official way in documentation.

In you example, you just need:

<md-toolbar>
    <div class="md-toolbar-tools">
        <div layout="row">
            <i class="fa fa-users fa-2x" flex></i>
            <h1 class="md-title" style="color:white">Org Chart</h1>
        </div>
        <span flex></span>
        <md-fab-speed-dial md-direction="left" ng-class="md-fling">
            <md-fab-trigger>
                <md-button aria-label="menu" class="md-fab md-accent">
                    <md-tooltip>
                        Actions
                    </md-tooltip>
                    <md-icon md-svg-src="img/icons/ic_view_module_48px.svg"></md-icon>
                </md-button>
            </md-fab-trigger>
            <md-fab-actions>
                <md-button aria-label="view" class="md-fab md-raised md-mini">
                    <md-tooltip>
                        View Chart
                    </md-tooltip>
                    <md-icon md-svg-src="" style="color:black" ng-show="cDP.read" ng-click="paneShowFn('read')"></md-icon>
                </md-button>
                <md-button aria-label="add" class="md-fab md-raised md-mini">
                    <md-tooltip>
                        Add Chart
                    </md-tooltip>
                    <md-icon md-svg-src="img/icons/ic_add_48px.svg" style="color:black" ng-show="cDP.insert" ng-click="paneShowFn('insert')"></md-icon>
                </md-button>
                <md-button aria-label="Settings" class="md-fab md-raised md-mini">
                    <md-tooltip>
                        Security Access
                    </md-tooltip>
                    <md-icon md-svg-src="img/icons/ic_add_48px.svg" style="color:black" ng-show="cDP.permission" ng-click="paneShowFn('permission')"></md-icon>
                </md-button>
                <md-button aria-label="edit" class="md-fab md-raised md-mini" style="color:black" ng-show="cDP.update" ng-click="paneShowFn('update')">
                    <md-tooltip>
                        Edit Chart
                    </md-tooltip>
                    <md-icon md-svg-src="img/icons/ic_edit_48px.svg" style="color:black"></md-icon>
                </md-button>
            </md-fab-actions>
        </md-fab-speed-dial>
    </div>
</md-toolbar>