Noticed my 08 ES350 recently making very loud noises coming from the engine bay. The sound kind of sounds like a loud vrooming noise, hard to describe (almost like the sound of those cars with loud aftermarket exhausts).

The sound is there on initial startup and gets louder upon acceleration. After the car is warmed up, there would be no sound while idling, but sound still very loud during acceleration. It seems the sound is correlated to the engine rpm?

I don't notice any power loss, no warning lights. Just the loud sound.

Any ideas what this may be?

 

could this be issue with exhaust manifold gasket?

 

Sounds like your exhaust has a leak, it's most likely the flanges or the flex joint. It looks like you're in Canada so it's even more likely the those parts rusted away and are letting exhaust gases through. When the pipes warm up, they expand and the leak goes away.
I had this happen to my exhaust system on a 98 ES300. The exhaust manifold gasket is less likely to leak as those areas are not exposed to the elements as much. Find a local exhaust shop that can find the leak and patch it up. They should be able to cut out the affected area and weld in a new section of pipe.

Flanges:




Flex Joint:

 

I went under the car and noticed the flange is pretty rusted, i think it's probably coming from there. Would using soapy water be able to tell if the leak is coming from there?

 

No, it is not like a leaking tire.
Instead, take a big shop rag or old towel and plug the end of the exhaust pipe (you may have to hold it in place) then listen for new noises that will indicate exhaust escaping from one of the rusted out areas. Also when you do this if there are leaks the engine idle speed will not change much.
If the exhaust is intact and you make a good seal with the rag, then your idle may drop due to increased exhaust pipe pressure from blocked flow.

There is a scene in the movie Get the Gringo where Mel Gibson sneaks behind the car of the guys tailing him and plugs the exhaust pipe with something he bought at the convenience store where they had stopped. Their car stalled out shortly after they continued to follow him.