I wear a compression vest under my tshirts such as this one
I am flying from London to Dallas soon and would like to know whether this will trigger airport security sensors to beep?
You can of course wear it. There are no regulation prohibiting clothes with metal parts in the cabin.
The metal detector may or may not be set of. How much metal is needed to set them of, depends on how they are configured. You will find metal parts on other types of clothes as well. Trousers or jeans usually have metal buttons or zippers and the detectors are usually configured to let a small amount of metal through, without raising an alarm.
If you wear such a compression vest and the detector beeps, there is absolutely no problem. You will be taken to a pat down or secondary screening, where you can explain the probable source for the alarm.