/^YBR069C\s+620/ is the regex expression to find "lines starting with YBR069C and having 620 separated by spaces", but your example line is not 1 line but 2, plus the image posted shows that the "starting with YBR069C" requirement is not well defined either. If you don't perfectly describe your input and your requirements you won't be able to find the appropriate results.

As it looks like you are interested in finding sequences with header lines structure of number label number, I would go for a printing flag solution to print every line under a desired header until the next undesidered header like this one:

perl -ne '/^\d/ and $p = 0; /^\d+\s+YBR069C\s+620$/ and $p = 1; print if $p' input.txt