Advice vs pros and cons of engine flush

I’m hearing a few seconds of “ticking” when I first start my car (1971 318 engine) - guessing it to be a lifter not getting enough oil. My engine was rebuilt around 1990 and I’ve only put about 60000 miles on the engine since then. Much of that time was spent parked mid-way thru that period. I’ve changed the oil a few time and always used detergent oil. Here’s my question: What is the risk of giving the engine a good flush? I’ve had it on the highway a couple of times in recent months - but not a lot of mileage during the past few years.