I will take a look at the flex joint and downpipe next I gueas... There's a muffler shop I usually tend to and see if they can spot something... I just think it strange... If I pin it in neutral, nothing happens... So if it were exhaust, why woild I have to be moving for it to be affected. 

Move got nothing to lose so I'll try there first. Thanks again

I was going to add that exhaust leaks can take on many different sounds.

As somone earlier has said, chirping is one of the sounds an exhaust leak can make.

my 2 pennies- 

Exhaust downpipe gasket leak . 

Assuming you have late model cast manifold - to the downpipe

= also too - downpipe has a flexy section under the braided woven part = could be broken too! Hard acceleration opens it up! 

I am really sorry to keep harping on this problem but its starting to drive me mad...

I had the car in to check out this problem. WHilst they were there, I had them replace the ball joints which were pretty hammered out... and replace the water pump to eliminate the play in the fan belt hitting the shroud. Even with this, the chirping persists and they can't put their finger on it. They said it might be the injector or fuel regulator but other than that... to inform them when I figure it out as they are stumped. THis is a good, reputable shop.

I have checked the valve clearance and confirmed with the shop that they are fine.

I have eliminated the fan belt and fan problem.

I have eliminated ball joints as the problem.

I have taken out the speedo cable to see if that was binding.

I have re-tightened the exhaust manifold studs to factory specs.

They took a look at the timing chains, it was fine. 

I have tighted all the rattley bits.

This sound is most apparent when I pin it from 2500 rpm and onwards. If I take it out of gear (and still moving) and rev it, there is no sound. If I put it in neutral and still rolling, no sound. If I put it up in the air, off the ground... no sound. If I am at a stop, no sound I am speaking of.

I will post a new video.

https://youtu.be/iynBIAeXPPc

Sound can be hear at :30... prominantly at :50 and at 1:16 before the wind takes over. 

The leak may only be present when appling load to the engine (starting off) with the engine rocking slightly especially if the stabilizer bushes are worn, and it may be why you don't notice it in reverse (rocks the other way).

what they did was stuff a rag in the exhaust pipe, raised the pressure, and listened for a hissing leak. Cheap diagnostic test

+1 to this idea!

I really do appreciate all of your comments.

Coincidentally, I had it at an exhaust shop while I was dropping my wifes car off. They checked it... there was a small hairline leak at the muffler that they patched. Other then that... they gave it a thumbs up.

I'll have a thorough look this weekend and report back. Keep the suggestions coming, they certainly arent hurting!

Its the higher pitched flutter that I am trying to deduce.

I hear a bit of a 'flutter'; it sounds to me like a leaking exhaust.

As it goes away once warmed up check all your exhaust joints for leaks.

The sound I am referring too is most audible between 40s-and 56s and again at 1:05... yes it does sound like a baseball card in spokes for sure. 

I do not have a breather on the valve cover. I have checked to see if the fan is hitting anything. It does seem to go away once the car is warm... and I have tried to ignore it... but its quite noticable!

Once you move outside the engine bay, a squeak could be anything that presents during forward motion: body (as shown), brake disks or dust shields, ball joint rubbers, lower arm bushings, upper arm bearings, shocks, tie rod bushings, seat frame.....

Take the fan belt off and see if the noise is still there.

It could ba an exhaust leak and a bad stabilizer bushing so not as noticeable in reverse due to the engine rocking the other way.

.... or the 'easy" solution to mysterious noises: turn the stereo up so you don't hear any strange noises.

If it is a plastic fan, they do warp with age and could possibly warp enough to graze something I guess.

Yeah, Im thinking something like that. Maybe as rpms increase plastic fan blades could deform and touch, but from the audio rpms don't sound very high. But why does he not hear it in reverse or when he revs it manually with the the bonnet up? Soft motor mounting wouldn't make a difference. As suggested, maybe a hose or something gets pushed with the bonnet closed, and the engine torque flex adds to it.

Timing cover breather, one or more fan blades hitting it.

I don't hear 'chirping" either, but at about 1:00 to 1:05 (time)  I can hear a rattle like someone fumbling coins in their pocket. Is that the noise?

Other than that, in forward gears, I hear a sound like a card in bicycle spokes that may be exhaust sounds, but to me sound like something rubbing in the fan. does the car have a side rad and fan on the water pump or a front (behind the grille) mounted rad? If you have a side rad and a palstic fan, check for it rubbing somewhere or something that may be coming in contact. 

I don't hear anything other than maybe a need for a valve clearance setting.

btw....it's "Rover MINI"  

Hi terry

Its an spi. I'll take a look under the hood and see if anything is suspect.