Is it appropriate to mention that authors refused to provide code samples when asked?
would be advisable to add a note that the implementation of THEIR algorithm is our implementation


Absolutely yes. This provides important context for your experimentation and as such, is valuable information for the reader.

Even better, you could make your implementation of their algorithm publicly available, so that future groups of authors will not encounter the same situation as you did (and will cite your paper).


  and that we reached out to them for their code and they declined?


That is the more delicate question to ask. It would surely be legitimate to do so, as it would represent the situation accurately. But such a statement has a social implication, which is that the authors appear in a slightly negative light (perhaps rightfully so). Proceed with caution.