Can I Upgrade SQL Server 2008 R2 Express to SQL Server 2014 Developer edition I currently have SQL server 2008 R2 Express installed for my QA/Dev environment on Amazon EC2 instance.

Now my database is growing beyond the 10GB limitation of Express edition, so am planning to buy SQL server 2014 Developer edition.

So can i upgrade my SQL Express 2008 R2 to SQL server 2014 Developer Edition, if yes what is the procedure?
No you cannot do inplace upgrade from SQL server 2008 R2 express to SQL server 2014 developer edition. Its not supported as per Version and edition upgrade supported matrix 

You can only upgrade to below using inplace upgrade method


  SQL Server 2014 Enterprise
  
  SQL Server 2014 Business Intelligence
  
  SQL Server 2014 Standard
  
  SQL Server 2014 Web
  
  SQL Server 2014 Express


But there is other option to do side by side migration. You install SQL server 2014 DEV edition. You backup your user database from SQl server express and restore it on SQl Server 2014.

You can migrate logins using This support article