I have a genomic DNA library digested with BamHI enzyme and ligated into a pUC19 vector. I am planning to amplify specific genes. Is it necessary to first add BamHI enzymes to release the genes from the pUC19 vector before doing amplification?
as it is done for the mitochondrial genome, nothing needs to be done to amplify or sequence sequences on your plasmide. In addition, by lack of chance, the clivage site can be inside your amplicon.
Nope, you don't need to digest the plasmid to release the insert. Just use primers that flank the ligation site.
Now, if you have trouble with the PCR, then you could use a rare cutter, check that is does NOT cut anywhere in your insert, and linearize the pUC19 vector.