Can I wear a bulletproof vest while traveling on British Airways from Heathrow?

Offically the answer seems to be yes. There's no mention of bullet proof vests (or any item of clothing) on the BA information page or restricted items document. Equally there's no mention in the Heathrow restricted items page.

However, I can see a great many practical problems that may be thrown in your way. Aside from the discomfort and inconvenience of wearing such a bulky item on a long flight, the following objections may be raised:

1. You are likley to be asked to remove it at security so that they can check you are not concealing anything. It's possible it would also set off the metal detectors
2. Cabin crew may require you to remove it for saftey reasons. For example, if the plane were to make an emergency landing on water, a bullet proof vest would see you sink pretty fast
3. There's no good reason for you to wear such a thing on flights. The risk of hijacking is already very low. The risk that hijackers would shoot a random passenger in the chest is even lower. However, security officers may take wearing such equipment as a sign that you intend to start a gunfight on the aircraft or within the airport, and detain you on those grounds.

Can't see how security will have a problem with a purely defensive device, but there are other considerations. Specifically:

It is of zero value to you during the flight. Anyone attempting to hijack an aircraft today will be promptly beaten to death by the other passengers. In the exceptionally unlikely event that someone does get a gun onboard, and they decide to target you specifically, the vest won't protect you from the headshot from about a foot away.

You say "hostile destination". I assume you have considered not going? Since you do not appear to be at risk at the departure point there is no point in wearing the thing there. If you are an official target then they certainly won't try anything on the airplane for the above reasons plus the bad publicity and the mess. Far easier to arrest you at immigration and use proper facilities, which every government has access to.

Attacks at the destination airport are possible if you are going somewhere particularly nasty, like Somalia. But a large group will use rifles, probably AK-47s in full auto mode. Most vests are designed for pistol rounds, and only 1 or 2. A full magazine emptied in your direction will cause enough peripheral damage that you won't survive without prompt attention from a class-1 trauma center, and anyplace that lets strangers roam the airport with machine guns probably won't have one of those.

A professional sniper will use a high-powered round from a distance - you won't see it coming. Even if they hit the vest, and you bought a good one with ceramic plates, the hit will knock you down and the next 2-3 rounds will be at your head. A first-class pro will use something like a M-82, which has a range of about a kilometer and won't even notice the vest.

If you are simply concerned with non-targeted crossfire then a vest is a good idea. But there aren't all that many gunfights enroute, so just leave it in your checked baggage.

And finally, if you have valid concerns that someone wants to get you specifically badly enough that they will try to hijack an international flight, security will probably deny you boarding on the grounds that your very presence creates a risk to the flight and the other passengers.