On a first pass, it doesn't sound natural. Here are some instances where "prospering" might be used. 1) "I hope you are having a "prospering" career "; "he had a prospering career"; "he will have a prospering career"; etc.) 2) "I hope you are having a prospering fiscal year", etc. 3) "It has been a prospering relationship", etc. I am not sure why exactly, "prospering progress" doesn't sound correct, but it could be due to the effect of alliteration. Conceptually, you can certainly describe a progress in some research as successful or "prospering". One would much rather use a different adjective in the example you cite. I would rewrite your sentence as the following : "I hope you are making great progress in your research."