8yo English Bulldog, skin irritation and hair loss Malibu Fires

We are fostering an English Bulldog displaced by the recent Malibu fires. We have had him for about 6 weeks and have noticed some new skin irritation spots and hair loss.  He has some scabbing and redness on his skin. The family said this is not the first time but they have not had it treated before.

When we took him in his whole environment changed (food, home, weather/season/sunlight, not to mention the extra stress of being uprooted so it may be hard to pinpoint an allergy.
Is there any topical treatment, or shampoo that may help?

Also, I am concerned if it could be mange or mites and a prescription may be needed.

He doesn't seem to be bothered by the spots, they don't seem to cause him pain or itchiness.

We do have another dog (12-year-old Bluetick coonhound) who is healthy and isn't showing any signs of skin issues.

The plan is to return him to his family when they find a new home, just trying to make him comfortable while he is here and maybe help him long-term.

Located in Costa Mesa, CA
Thank you!

Here is his family and their old home