"amazingly modern" is correct and usable in written English.
You might use it in a sentence where you are describing something that is modern and surprising. For example, "This new shopping mall is amazingly modern."
This show of ancient Chinese ceramics and tomb sculptures has neolithic pots from 6000 B.C. that look amazingly modern.
These intensely beady stories and sketches – a blend of fact and fiction – are amazingly modern, as easy to devour as, well, a box of chocolates.
Thurston is a genius with felt, using this ancient fabric in amazingly modern ways to make eclectic shawls, mufflers and hats.
It is not traditional food at all, but amazingly modern Spanish cooking – but they insist on using ingredients from the immediate area.
The French sinologist Jacques Gernet is of the opinion that Shen possessed an "amazingly modern mind".
You will never again use the phrase "happy medium" without thinking of this amazingly new, thoroughly modern Madame Arcati.
(Amazingly, to modern sensibilities, state and federal governments were able to undertake surveys of this sort without any debate in state legislatures about their right to do so).
It's no longer universally acknowledged that "a single man in possession of a good fortune must be in want of a wife", but many of Jane Austen's thoughts on love, relationships, class, clothes and even the joys of nature are amazingly relevant to modern life.
Amazingly, the study of modern languages in the UK continues to decline.
And the company now has a version of Pages that runs amazingly well in any modern web browser, even on a Windows PC.
No, this is not the continuation of some long-standing tradition, but amazingly a creature of modern politics starting in 1994.
