You can combine RNAzol with chloroform. You may want to know that there is an improved version of RNAzol called RNAzol RT which uses a unique formulation of phenol and guanidine thiocyanate that effectively separates RNA from other cellular components without the need for a chloroform-induced phase separation to achieve pure RNA extraction.
The chemical composition of RNAzol RT allows for direct RNA precipitation without the need for a separate organic phase created by chloroform in a single step, meaning the process is quick and efficient.
If you may want to use RNAzol RT, then you may isolate RNA from samples without the use of chloroform in a single step.
I usually used RNAzol RT for bacterial RNA exctraction, but there were always some portion of DNA. That´s why I would like to try to add chloroform step. The manufacturer recommands bromanisole. But is it a mistake to choose the addition of chloroform step to better separate RNA from DNA, even if manufacturer declare that it is not necessary, please?