I found nothing specific to clothing issues of the 36th US Infantry in US National Archives, RG 107 (Sec of War corresp), which is not unusual as clothing could be sent via regional arsenals/clothing depots. But from the following notes, you will find that the 36th probably had difficulties in recruiting, dress, equipmenet and possibly discipline.
1 November 1813 - 200 men to Annapolis MD, remainder to Frederick.
10 December 1813 - 572 strenght, in Maryland
17 June 1814 - has arrived at St Leonard's Creek, men exhausted, lacking camp equipage,
19 June 1814 - marched on to Paxtuent on 18 June, men in terrible shape
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