Squirrels will eat right through those mesh bags; they know how to
destroy just about anything. I found old nylon stocking stretched
over the sunflowers will deter the birds but as far as squirrels I use
a Havahart trap regularly and make regular "deposits" on the other
side of town.

Ask everyone you know (including yourself) to save those mesh bags that
onions come in. Put them over the developing flowers and tie with any
non-plastic string. Ugly, but they work.