[ixth]

Возможно, флажок in_progress сработает.

$(function(){
	var in_progress = false;
	$('#my_form').on('submit', function (e) {
		e.preventDefault();
		if (in_progress) {
			return;
		}
		in_progress = true;
		var formData = new FormData(this);
		var $that = $(this);
		$.ajax({
			url: $that.attr('action'),
			type: $that.attr('method'),
			contentType: false,
			processData: false,
			data: formData,
			dataType: 'json',
			success: function (json) {
				in_progress = false;
				var messageResp = ['ок','не ок','длинно']; 
				rel_q();
				$('#uploadImage, #message').val('');
				$('#resp').text(messageResp[json]).show().delay(1500).fadeOut(800);
			}
		});
	});
});