There was also a Robert Hale buried 22 Nov 1665 at Faversham, Kent, England.
Do you have a specific city in Kent where your Robert Hale lived or died?
In your question, you indicated that Robert's father had been shown as Henry, Thomas, Richard or Charles.
Ancestral file shows only one of those names at https://familysearch.org/pal:/MM9.2.1/SBFQ-RT2 It's Henry Hale born about 1589 at Kent, England. Ancestral File info is only as good as the accuracy of whoever submited it.
Extensive historical record collections for the UK can be found at: familysearch.org/search/collection/list#page=1®ion=UNITED_KINGDOM_IRELAND