Does getting dental fillings increase the risk of developing prostate enlargement?

Not likely. Never heard of any association of the two, much less a direct link. Cannot imagine how they could be related. You might check online for any info. Good Luck.
Prostate Hyperplasia. Exact cause is unknown, but most likely due to hormones and growth factors, none of which are remotely related to dental fillings.
Pseudoscience. There is no evidence that shows any correlation between having dental fillings and increased risks for prostate enlargement. Ask your dentist for more information.
No. I know of no medically proved connection in which dental fillings may cause prostate enlargement. The chemicals released by silver (amalgam) or white (composites) are so low that our exposure through diet (of similar or same chemicals) is higher.
Where and how... Where and how did you get the idea described in this Q? If you can let the world know about where and how, I or may colleagues may look into it in detail. Nonetheless, I have never read or heard anywhere in my 46-yr study and practice in urology. So, up to this moment, I would not think there is such a connection.