I have done small code to keep multi-selection between pagination and also during refresh.
    $("#searchPhonoList").flexigrid($.extend({}, flexigridAttrs, {
        url: './rest/phono/search',
        preProcess: formatSearchPhonoResults,
        onSuccess: successSearchPhono,
        onSubmit: submit,
        method: 'GET',
        dataType: 'json',
        colModel : [
            {display: 'titre', name: 'titre_brut', width : 240,  sortable : true, align: 'left'},
            {display: 'version', name: 'version_brut', width : 60,  sortable : true, align: 'left'}
        ],
        height: "auto",
        sortname: "score",
        sortorder: "desc",
        showTableToggleBtn: false,
        showToggleBtn: false,
        singleSelect: false,
        onToggleCol: false,
        usepager: true, 
        title: "Liste des candidats",
        resizable: true,
        rp:20,
        useRp: true
    }));  
    var searchPhonoListSelection = new Array();
    $('#searchPhonoList').click(function(event){
        $(' tbody tr', this).each( function(){
            var id = $(this).attr('id').substr(3);
            if ( searchPhonoListSelection.indexOf(id) != -1 ) {
                searchPhonoListSelection.splice(searchPhonoListSelection.indexOf(id), 1);
            }
        });
        $('.trSelected', this).each( function(){
            var id = $(this).attr('id').substr(3);
            if ( searchPhonoListSelection.indexOf(id) == -1  ) {
                searchPhonoListSelection.push(id);
            }
        });
    });
    function successSearchPhono() {
        $("#searchPhonoList tbody tr").each( function() {
            var id = $(this).attr('id').substr(3);
            if ( searchPhonoListSelection.indexOf(id) != -1 ) {
                $(this).addClass("trSelected");
            }
        });
    }