Change ui to:
ui = bootstrapPage(mainPanel( div(class = "row", div(showOutput("chart2", "Highcharts"), class = "span4"), div(showOutput("chart3", "Highcharts"), class = "span4") ), div(class = "row", div(showOutput("chart4", "Highcharts"), class = "span4") ) ))
Add bootstrapPage to tell brilliant about using the bootstrap library. See http://getbootstrap.com/2.3.2/scaffolding.html for an overview of scaffolding. mainPanel has a width parameter, which defaults to 8. This is span8 in bootstrap. The above code is not perfect, but hopefully its beginning.
EDIT: for full screen
ui = bootstrapPage(mainPanel(width = 12, div(class = "row", div(showOutput("chart2", "Highcharts"), class = "span6"), div(showOutput("chart3", "Highcharts"), class = "span6") ), div(class = "row", div(showOutput("chart4", "Highcharts"), class = "span6") ) ))
Note that mainPanel (..., width = width) is just a handy function for divs with widths.
Screenshot:

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