Unfortunately our home has only 5/8" OSB subfloor instead of the recommended 3/4". Due to different transition areas we cannot afford to go much higher than an additional 1/4" for the subfloor. What do you recommend we do to prepare the subfloor correctly for the Engineered Clic flooring. We will either be getting 3.5", 5/8" planks or a 5", 3/4" plank depending on what we have to add to the current subfloor.

You are fine with the 5/8 as long as it it flat and down solid. You could staple down 1/4 in if you want but I don't see any reason for you to spend any extr money if you don't have to.

Since you are putting in a floating floor, there is no need to beef up the subfloor to meet nail down standards.
As Jeff says, make sure the existing subfloor is flat and secure. Sand down high areas first, then pack low areas with any suitable levelling compound, felt paper, or shingles; depending on the degree of irregularity you have.