I may be wrong, but my understanding was that the British attack was lauched in low hanging mist/fog. That all that could be seen was the British flags above head high and the rifleman fired before the distinct targets could be seen until they got close. That the reason that Paxton was as close as he was, and being on a horse, was because he was trying to direct the battle and could not see what was going on.
And yes the red Jackets did make a fine target along with the white Cartridge Box and Bayonet straps, which made a fine "X" right over the heart. The common story is that the British wore those red coats was so that the enemy wouldn't see them bleed.