Pictures of buildings mentioned in the second edition “Suffolk” volume of “The Buildings of England” series by Sir Nikolaus Pevsner.

There is no church in the entry for Flatford. Pevsner says "The three principal house are the Manor House (Valley Farm), the Mill, and Willy Lott's Cottage; all pleasant to look at, but visited chiefly for their connection with John Constable." Willy Lott's Cottage and the Mill are timber-framed and of the C16; the mill is of brick and dates from the C17".

Here is the Manor House (Valley Farm):
Stacks Image 15
And here is Willy Lott's Cottage:
Stacks Image 11
And now three views of the Mill:
Stacks Image 27
A bit closer:
Stacks Image 23
And from the rear:
Stacks Image 17
John Constable's famous Haywain painting evokes Suffolk and is nominally set at Flatford and the millpond by the River Stour but was actually composed in his London studio based on drawings taken over several years. More details at the National Gallery site.