I recently found a Burji to English dictionary and am linking to it here (and here just in case the first link doesn't work). It's by R. Dame and C. Wedekind.
Krista in Georgia has also created an English to Burji version. The link is here.
Initially our tutor had told us that Burji was similar to Amharic, but after looking into it we found they are very different languages. Burji is Cushitic while Amharic is Semitic. The boys' paperwork says that they know both languages, but we'll have to wait and see if that is true. For now we are focusing on Amharic because it's a much more widely spoken language in Ethiopia.