How to fetch data in chunks with SearchThingsByTemplate method

There isn't an standard way of doing it.

But, when you say from your server to your system what does you mean? Becouse the cose you are showing here it's Javascript server side snippet which runs on the same server.

Few recomendations:

Whenever you can use ThingTemplates["ThingworxTemplate"].QueryImplementingThings(); which it's a way faster than SearchThingsByTemplate one. For instance this code it's faster than yours:

var result = ThingTemplates["ThingworxTemplate"].QueryImplementingThings({
 maxItems: undefined /* NUMBER */,
 nameMask: undefined /* STRING */,
 query: undefined /* QUERY */,
 tags: "TWX:RuntimeData"
 });

Then the speed problem it's on the connection side and you must transfer data in chunks you will need to implement a custom service on source where you pass PageNumber and PageSize and return the desired rows.

Something Like

var thingTemplateName = "ThingworxTemplate";
var taggedWith = "TWX:RuntimeData" 
var Entityresult = Subsystems["PlatformSubsystem"].GetEntityCount({ type: "Things" });
 var maximumThingsCount= Entityresult.count;
 var startItems = PageNumber*PageSize;
 var maxItems = startItems+PageSize;
 var tempResult = ThingTemplates[thingTemplateName].QueryImplementingThings({
 maxItems: maximumThingsCount,
 nameMask: undefined /* STRING */,
 query: undefined /* QUERY */,
 tags: taggedWith
 });

 result = Resources["InfoTableFunctions"].CreateInfoTableFromDataShape({
 infoTableName : "InfoTable",
 dataShapeName : "RootEntityList"
 });

 for(var i=startItems;(i<maxItems)&&(i<tempResult.rows.length);i++) {
 result.AddRow(tempResult.rows[i]);
 }