Hello, any sort of 5mm LED should work just fine, but may not exactly match the color, brightness, and viewing-angle of the included LEDs. We purchased our LEDs directly from the manufacturer in China, so I don't think they have a normal part number at Digikey or Mouser.
If you want, we can mail you some replacements. Please fill out the contact form, and be sure to include your complete mailing address, the exact kit you have (SMT? Red? Blue? etc.), and how many LEDs you need. Thanks!