If you bore into the chimney brick, install anchors and lags with a long large heavy mast and the chimney is in bad shape already, maybe, sort of, probably not. If anything a chimney strap mount will hold your chimney together better that without it. You can't damage a chimney with a strap mount except for the sharp edges at the corners where it might rub down a sharp brick edge. For anything other than soft red bricks it shouldn't hurt the chimney material.
My father having built and installed many brick chimneys built me a chimney antenna mount as a kid and it had bent and formed 1/8" steel sheet metal corner brackets for the mast U bolts and used 3/8" steel cable and large turnbuckles instead of flat straps. It also had short pieces of steel angle stock at the corners of the chimney where the cable wrapped around. I cranked the turnbuckles until the steel cable was like a guitar string and it was up for many years with a 21ft galv steel fence rail and a 22ft tall Hy-Gain Penetrator on top of that. With the mounts about 4 or so feet apart and the antenna slid about 1ft down on the mast that would be about 38 feet of antenna and mast sticking up unguyed. It was beautiful, although not something I would do now.
I would suggest you find some other place to mount your antenna on. Using your chimney can cause it to crack from the constant vibration the antenna will place on the structure. Given enough time and vibration could cause a major failure and have it topple over in high winds.
This is a common problem that people only find out about down the road with the possible damage to the building. It also could cause a problem with the insurance claim when they ask if you had an antenna mounted on it.