Well, you have not revealed either what power amplifier you are taking about or what current rating it needs, so it isn't really possible to offer any particular comment.
Are the connectors at each end rated for the current you amp needs? Is 18GA sufficient for "longish" (whatever that means?) at the current your amp wants? It is easy enough to find an online website that will tell you what wire gauge is required for a particular current over a particular distance.
Observe (UL_info) that the vendor acknowledges that NO cloth-covered cable (including theirs) is UL-Recognized. It is not likely to cause trouble PROVIDING YOU SIZE IT PROPERLY!!!. However if there IS any trouble your fire insurance is likely forfeit. That seems like a very BAD tradeoff for the looks of a vintage power cord. YMMV.
If you do the job properly there won't be a problem.
If your handiwork starts a fire (unlikely) then the insurance cover will probably be questionable regardless of whether you used UL listed parts or not. The cloth covered wire looks so much more robust than some of the thin 2-core cable on cheap appliances.
There must be some source of UL listed cloth covered cable. I think irons still come with cloth covered cords. They are round and don't really have the retro look though.
Searching online I came across someone who had used climbing rope (woven kernmantle rope) to cover modern cable. They stripped the core out of the rope and put the braid over modern power flex. If I wanted the retro look I'd probably just use the cable from the website.
The Sundial cloth covered cable is made in the United States (it's still "imported" if you live in the UK) and uses polyvinyl chloride insulation, unlike the old 1930's cloth over natural rubber which becomes brittle and dangerous. Non-cloth covered PVC insulated wire is "today's most widely used electrical insulation material" . It's very unlikely that adding an additional layer of braided cotton or rayon fabric over the already excellent insulation poses any additional safety issues compared to a much more common single layer of PVC.
Wire of 18 ga. is rated for 2.3 amps for continuous power transmission applications. That's 265 watts on 115 volt mains. Even an old, inefficient 50 watt guitar amplifier won't be using anything like that much power. It's unlikely the amp will draw more than 1 ampere average current.
25 feet (8 meters) of 18 ga. 2-conductor power cable will have a total drop (calculated from the resistance of both conductors in series) of 3.15 volts(@1 Ampere). That slight line drop should easily be tolerated by any guitar amp.
The inductance created by ugly Ferrite beads have will have much more RFI rejection than the cool, retro cotton or rayon covering which only blocks pre-1960 radio waves. Unless you have known radio frequency noise sources nearby, or noisy stage lighting dimmers, there is no need for ferrite beads on a power cable, and besides they ruin the whole retro look. Note: If you use a weave-covered power cable, a woven guitar cable is mandatory or you'll drop your coolness factor by at least 6 dB.