Using Access Web application I would like to use a custom search form to select data and then export it to Excel. I have done this in client Access using TransferSpreadsheet, but there is no such thing in web app.

You are right. There isn't a way to export a spreadsheet from an Access web app into Excel. What you can do instead is create an Excel workbook and link it to the datasource you want to use in the SQL Server -- or SQL Azure -- database behind the web app. The Excel sheet can be put into a document library on your SharePoint site for sharing with users. We discuss this approach in the book.