Hello! This protocol seems to me to be the standard protocol for RNA extraction from tissues. I believe that for PCR product purification, it would be more interesting to use a column-based kit. Additionally, if it is a DNA purification protocol based on phenol/chloroform, there are some modifications. Other reagents such as isoamyl alcohol, ammonium acetate, and glycogen will be necessary. You can easily find a protocol that meets your needs by searching for "Phenol/Chloroform for DNA Purification", however, I would still recommend using an appropriate kit such as the PureLink™ Quick Gel Extraction Kit from ThermoFisher.
I agree with Clei Endrigo Piazza and Katie A S Burnette. A kit will save you the hassle of dealing with toxic chemicals and waste collection.
As a note, this direct PCR product cleanup is most suitable for PCRs giving a single band. You'll need to run some of your PCR on a gel to check it first. There are also kits for DNA cleanup from gels so you can excise a band of interest.