Those pictures are not close enough to tell about fungus, but it's not chinch bugs. Chinch bugs always start at the hottest part of the lawn. Usually that is the corner where the concrete sidewalk meets the concrete driveway in full sun.

Here is a picture of a "normal" St Augustine fungus.

The tan lesions with brown borders are common. I cure that every year with ordinary corn meal from the feed store. 50 pounds should be well under $10. Application rate is 20 pounds per 1,000 square feet. It takes 3 full weeks to see the improvement. You'll see new grass coming in fully green and not getting the disease.

The cause is too much water and/or lack of air circulation for days at a time. For example if you put a piece of cardboard on the grass and pick it up a few days later, you'll see these disease spots underneath.

I have Floratam St Augustine in full sun. It grows so fast it literally outgrows the fungus. It still looks bad, but it never seems to die out like other varieties did.