You could do that. What you'd have to figure out would be how long one would last. If you know the battery rating in amp-hours and the current draw of the vest, you could calculate the endurance. The newer lithium iron batteries would be the ones to use because they are more efficient.
2015 BMW R9T, 2010 Ducati 1098 Streetfighter S
2009 Kaw 650 Versys, 1967 Triumph 650 TT Special