A tall order! Have to say at the outset that none of the sites I've found have all the plant names. Here are the links I've amassed/bookmarked over the years. I think there's one or two that teach you how to pronounce Latin (the basics & all the rules), but not just botanical. That can get a bit complicated though.

Oh! Actually, it might be in your best interest (as I've found it works better) to know how to spell the plant names. You can pronounce them however you want that way (LOL) in order to write them on paper to show someone what you want!

This 1st one for self-pronouncing is broken up into 4 sections, but you can always backtrack to the original site for more info on other stuff (by deleting the last part of the URL up to the last slash mark (/).
A thru D
E thru L
M thru P
Q thru Z

Fine Gardening Pronunciation Guide
Home Grown
How to Say It
Pronunciation of Botanical Latin
You can click on speaker icon to hear some plant names

Several of my links were old & no good anymore~oh well!
HTH! Also remember, there will always be others who insist on pronouncing it a different way than you. That's okay, as long as you understand which plant you're talking about!
~Rosemarie

Rosemarie,

Thank you very much for the amazing list of websites. Those will come in handy and I appreciate you taking the time to list them all.

Larry

For hardy shrubs and trees, Go here. On each species, click on the little music symbol at the top. Once you hear a variety of latin names you will be able to pronounce most plant names. Of course different people pronounce them differently, and usually not as a latin scholar would ;)