My bad. You were talking about spike protein the whole time, and I thought you were asking about the mRNA.
Spike protein induced by the vaccine mostly stays in and around the injection site, although some does reach the plasma and some gets to the liver via the bloodstream.
Proteins are also broken down eventually, but the process takes longer, probably a few weeks.
Studies were done on spike protein distribution after injection, so the information has been known for a long time.
The spike protein induced by the vaccine differs considerably from that produced by the virus, as it has been conformationally stabilized to limit its interaction with ACE-2 receptors.
There have certainly been studies that showed spike protein can cause vascular inflammation and even myocarditis. Vaccine spike protein does not seem to induce the same responses in target tissues such as vascular endothelial cells or myocardial cells. There are several studies on this that you can find and read.
Production of the spike protein in your body after vaccination is limited to just a few days because of the breakdown if the mRNA that I mentioned before. The protein itself, though, takes a few weeks to be degraded. Fortunately, it us in a different form. Not only is it stabilized, but it retains anchor proteins, which cause the cast majority of it to remain embedded in the cell wall rather than circulating through the bloodstream. The small amount that does go into the blood tends to go to the liver, as would be expected, where it also tends to anchor to cells before it is degraded over the course of a few weeks.
I apologize again for misreading your original post and thinking you were talking about the actual mRNA.