McCollin put K's 2-0 up in the first half and missed several chances to complete a hat-trick. He was not the only culprit.
Burnham, who pulled one back before half-time through Josh Webb, had their chances as well but could not punish K's for their wastefulness.
Sunday's other tie was a 0-0 draw between Cray and Arlesey at Hayes Lane, thus completing an unbeaten weekend for the Ryman League in six Trophy meetings with Southern League clubs.
The sides try again at Arlesey on Tuesday, an unwelcome distraction for the Bedfordshire side in the run-up to their FA Cup visit to Coventry on Saturday.
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