A. were reading challenging material, they will be more likely to read on their own and gain proficiency quicker than will
even if we ignore the tense change, children (noun) ...,than will (helping verb). parallelism issue
also "more quickly" would convey the meaning better than "quicker"
B. read challenging material, they are more likely to read on their own and gain proficiency quicker than will
same as A
C. read challenging material, they are more likely to read on their own and gain proficiency more quickly than
seems fine.
D. were reading challenging material, they have been more likely to read on their own and gain proficiency quicker than will
same as A
E. were reading challenging material, they are more likely to read on their own and gain proficiency more quickly than
now here the tense change .
C conveys the meaning better
IMO C