Pre covid, flight centre used to offer the lowest price guarantee - has any one had any luck with price matching since then?
I often see FC deals which have an additional booking/service fee, so can't imagine they have much flexibility…
The likes of sky scanner offer pretty good rates, but would prefer to go via flight centre to use up some rewards dollars.

For long haul flights, I always find a 'good price' online, then go into a travel agent and see what they can do. Often they are able to beat the price, and you also have the benefit of having someone to assist who is likely to go the extra mile (!) if anything happens. I do tend to avoid the very low cost airlines though, so if you are going that way, maybe the agents won't be able to compete.
However, for local or just trans-Tasman, I tend to book direct on the airline website.