In a word.....no. This comes from personal and professional experience, my job means I know to much about this subject as some on here can attest to [emoji6].
Engine flushes came into existence at the time of Mineral oils. Mineral oils are basic lubricants which are only mildly refined from crude oil base stock. Their molecular structure is unstable and un-uniform, they do not handle temperature well, there's always a percentage of contamination from other particles, they have poor oil film strength and overall were rather average. Mineral oil, when exposed to certain conditions are known to cause varnishing, coking, carbon deposits and high wear.
As such flushing came into play as a way of removing those deposits and engine contamination using very strong solvents and caustic chemicals as a stripping agent. Solvent agents such as these have three main issues.
1)Solvent bases ALWAYS cause oil film instability and increase shearing and they reduce the oils physical lubricity.
2) They often cause deposits to break off into chunks or flakes, they do not dissolve into the oil for the most part.
3) As a result of their effects on lubricant protection, they often have nasty additives such as high zinc and sometimes PTFE to counteract the wear that they can cause. These are very bad for modern emissions systems are are one of the reasons for the huge variance of ACEA grades and manufacturer certifications to prevent oils that are made for one engine being used in another that it can damage.
In the engines that these flushes were normally used in, they had some benefits (not many mind you) and as the manufacturing tolerances of these engines were quite slack simply because that was all that was possible at the time, loose contaminants and gunk that was removed by the use of a flush tended to not cause the degree of damage they do in a modern engine. They also didn't have the advanced emissions systems of today's engines.
In your case, the Twinair is a small displacement, hot running, forced variable vane induction engine. It had a cast iron block, aluminium cylinder head with short but narrow oilways which are designed to increase oil pressure and feed force and is manufactured to tolerances that even 10 year old engines can struggle to match. It also runs on group 3/4 synthetic oils which are broadly incompatible with most flushing solvents due to a risk of acidic attack and 'potting' where they can effectively jellify if mixed with incompatible products.
Say you bunged a bottle of flush into your engine, some carbon deposits flaked off and were circulating around your engine. Those deposits if they because caught in a bearing, oil ring or a oilway could cause localised scoring, severe wear or even oil starvation which is very bad news & would shorten your engines life by a huge degree. If they got into the turbo you could expect temperatures that would cause the deposits to react, they could get into the bearing assembly and cause failure. (consider that solidified carbon is as hard as diamonds in some cases)
Along with this, the particles if they flaked off to a large enough degree could block the filtration medium of the filter causing oil starvation of the whole system or opening the oil bypass valve in the filter causing unfiltered carbon filled oil to move around the engine unchecked.
The one thing that must always be kept on mind, is that of the dozens of OEM's, hundreds of Lubricant manufacturers and blenders and the many labs who test these products all have common......is not a single one recommends flushing. In fact most actively discourage it. Engine technology has moved on so much, tolerances are better, lubricants are a world apart from where they were a few years ago and the only thing these additive companies have in their favour is the hope they can convince the consumer that they know better than the people who make engines and oil. It's all marketing.
I agree with JRK and others, get a good quality engine oil and a quality filter. Make sure it fits the correct spec, drive it *ahem* briskly and then change again after 500 to 1000 miles allowing it to take as much crud out of the engine as it can, modern synthetics all contain cleaning agents but they work in vastly different ways to flushes and work gradually preventing the issues above. If you need any advice on the lubricants and filters, give me a shout. Ill do what I can to help [emoji106]