How much depth, front to back, is there from the fence to the patio and is the wooden fence we see one of the gates you mention?

Wooden gate yes it’s only a gate like that on both sides .

The metal fence is about 30 feet from the wooden gate to the back of our garage(converted efficiency) from the fence to the patio.. do you mean the patio screen door ?

I meant how much depth back to front is there in the grass planting area along the cyclone fence. It determines what size shrubs you could plant there. Ideally, if you the area is at least 12-15 feet deep, you could plant large shrubs that would give you the privacy you want.

8What zone are you in - do you need privacy year around? Will make a difference on the type of shrubs (tall and full) or arborvitae planted close together, in any case if you need immediate privacy it will be a considerable investment.

Have you considered adding privacy slats to the chain link fence?

Privacy slats that sounds great.

I’m not sure about planting shrubs because they would take up too much space and I’m guessing bring in more insects. I’m in northern Florida.

As an idea IF privacy on your screened porch is desirable, We installed roll-down shades on our covered deck. These will extend down as much as 6 feet.

In Florida you’d want shade even more than privacy, no no? If you can use shrubs to cover the lower five feet you can add a small tree to give you shade. Talk to the neighbors about the kind and siting as they may be grateful to have it.