It says Lucky Miillander Band. Is he just fronting it?
Lucky Millinder became the leader of the Mills Blue Rhythm Band in 1933 and its last records were even released as Lucky Millinder With Mills Blue Rhythm Band. The tune in the video is Ride, Red, Ride which was recorded by MBRB in 1935. Lord lists the video as being from 1938 and says "Personnel of the band at this session may be that of the Mills Blue Rhythm Band of the period which Millinder had led prior to taking over the Bill Doggett band in May, 1938.". Since the personnel is unknown I guess I can't say for sure, but it's worth noting that Lord lists another tune from the same film short, Jazz Martini, which was another MBRB tune, originally recorded in 1933.
Millinder's own successful band wasn't formed until the early 40s, btw.