It is my understanding that omission of prepositions used with certain verbs is becoming increasingly accepted. I was even corrected by a proofreader when I wrote "fleeing from country X" instead of "fleeing country X." Is this BrE/AmE difference, where AmE is more flexible than BrE? Is there a list of verb-preposition pairs whereby such an omission is accepted? For example, in the following sentence, "Moore and many other evangelical Christians spared Trump their censure," would it be correct to put a preposition for or of between Trump and their, so that the sentence reads "spared Trump from/of their censure"? Thanks!
In most cases, you can figure out if you need a preposition or not by checking a dictionary. I looked in several Oxford dictionaries; for both words (flee and spare) it's the same definition for both ODO pages (English vs. American English) plus NOAD, indicating that for these two words, there is no significant difference between AmE and BrE (but I'm sure that this isn't the case with all words).
You can see that both "fleeing from country X" and "fleeing country X" are correct from these definitions of flee:
[NO OBJECT] 1. Run away from a place or situation of danger.
1.1 [with object] Run away from (someone or something)
The only real difference between these two definitions is the number of objects they take (so I'm not sure why a proofreader would have changed it). Definition 1 takes no object (as in "fleeing from country X"). Definition 1.1 takes an object (as in "fleeing country X").
Also, look at these definitions of spare (verb):
2. [with object] Refrain from killing, injuring, or distressing.
2.1 [with two objects] Refrain from inflicting (something unpleasant) on (someone)
Definition 2.1 is the definition for your second sentence. It says "with two objects", and your two objects are "Trump" and "their censure". Using a preposition would be grammatically correct, but it would make it fit definition 2 (there isn't really a difference between these two definitions though apart from the fact that they take a different number of objects).
Is this a Modern English thing? Not really, flee for example had both transitive and intransitive forms in Old English:
Ða hyrdas witodlice flugon.
West Saxon Gospels: Matthew
Wæs him ut myne fleon fealone stream, woldon feore beorgan, to dunscræfum drohtað secan, eorðan ondwist.