Will installing Flash cause any harm to my computer?
There are no known issues associated with installing Flash.
Oh, you meant aside from the annoying animated ads that you’ll now see on every other goddamn web site? And other than the fact that you’ll be annoyed to no end by promotional and marketing sites which think it’s K3WL to hide all their content in Flash, so none of it can be indexed by search engines, and you can’t actually use your known-good browser interface to view the site, and instead have to navigate through whatever hideously unintuitive scheme their overpaid script kiddies crazy-glued together after smoking up all weekend?
No, no known issues at all.