Thanks!

So, TIL that the English term "flower" is used in a much broader sense than its supposed direct German translation "Blume".

Nobody in Germany would say a tree has flowers (Blumen), but that it has blossoms (Blüten).
And "Flowering Plants" are also named "Blütenpflanzen" ("Blossom Plants").

So saying "tree flowers" sounds really, really odd to me.
Like someone calling a jumping frog "a flying frog".

So thanks for the explanation, would never have guessed that by myself but will now use it in all my future tree-related discussions! :-)