Some journal' editor said that "the authors should provide proof that the paper has been proofread by a native English speaker". Is this a reasonable request?; if yes, How can I provide it.
This seems strange to me. Do they demand this also from native speakers, and how they distinguish between native and non-native? Normally, the editor should see from reading a few paragraphs of the paper whether the language is good enough. However, you may attach a short declaration by the native speaker that he/she read and improved the paper. Generally, it is wise to give the paper to a native speaker, even when this is not demanded - see this discussion: https://www.researchgate.net/post/Why_is_it_compulsory_to_have_native_English_reader_checking_what_we_write_for_publication_in_western_journals . See also these discussions on translation tools which may be helpful:
Agreed, usually this should be possible to evaluate by taking a look at the paper. If actually a document is demanded, a short note by the proof reader or an invoice for such services (if used) should suffice. Considering that authors are often economically exploited by journals in the first place, it would be better if they agreed to provide proofreading by a native speaker for all submissions.
If the journal insists, it's possible to get a digital record of the proofreading. This can be done easily using a simple tool like MS Word. However, I agree with the previous gentlemen. It seems strange for them to make such a request.