Mr. Frank Churchill is summed up nicely by Mr. Knightley as, “…a most fortunate man…Everything turns out for his good.-He meets with a young woman at a watering-place, gains her affection, cannot even weary her by negligent treatment…His aunt is in the way. – His aunt dies. – He has used everybody ill-and they are delighted to forgive him." (295)
Mr. Churchill is the most gallant of all the men in Emma, and he is a trickster. He is also the only other man Emma slightly considers for courtship, besides Mr. Knightley. Eventually Emma determines that she doesn't really want to be with him, but only after fantasizing about how their relationship would end, and some sage words from her father, Mr. Woodhouse.
In terms of likability, Mr. Frank Churchill is a lot like Emma in character. He is vain, mischievous, and of a fantastical romantic nature, traits we can also see in Emma. Although he does get up to shenanigans (As Mr. Knightley points out) we are still compelled to like him despite his character flaws. And also like Emma, perhaps we are more inclined to like him because of these flaws. Regardless, as Mr. Knightley points out, we like him (and probably Emma too!) more than they really deserve.