Translation:Please talk slowly.
遅い has a negative or neutral feeling. Like のろのろ. It carries a feeling of laziness or dumbness. Or it just means slow as opposed to fast.
ゆっくり has a positive feeling. It means slow down, relax, take it easy. I has a feeling of gentleness and kindness, being careful and mindful.
If it is the verb 話す (はなす) then, when conjugated, the okurigana is always necessary. You will always conjugate it as 話します or 話して. If you are using the noun 話(はなし) then the okurigana is not necessary. For example: その話を聞きました (I listened to the speech). If people are speaking more formally they will frequently say something along the lines of 彼はお話をしました (He gave a talk)
‘Slow’ can be an adverb as well as an adjective. Not all native speakers know this and some will tell you it’s wrong to say “speak slower”. However, both “speak slowly” and “speak slower” are correct in terms of grammar, with the latter being considered more informal or casual. Granted, a more suitable alternative to “speak slower” using the word ‘slowly’ would be “speak more slowly”. With regards to the japanese sentence in question, as there is no context, one can assume that the statement implies the listener has not heard yet from the speaker, therefore the translation corresponds more to “Please speak slowly” rather than “please speak slower”, which is translated as “遅く話してください" (osokuhanashitekudasai) with ‘遅く' (osoku) meaning ‘slower’. I hope this clarifies things. I had the same answer as you which is why I felt the need to comment. What surprises me though is the fact that people would down-vote a comment rather than explain their observations.