If they were using a rifle, they had to measure the powder if they wanted the powder charge to be the same for each shot: that was critical to accuracy. For that, they would use a powder horn and a measure. For a musket, accuracy was not critical: rate of fire was. Every soldier would have a large leather cartridge box on his belt. Inside would be cartridges, which at this time meant a charge of paper and a musket ball wrapped with paper. The soldier would grab a cartridge, bring it to his mouth, bite down on the ball ( recruits needed to have a couple of teeth, in order to do this) and pull the cartridge away, tearing the top off. He would pour some of the powder into the pan of the flintlock, and close the frizzen. Then he would cast the gun about, pour the rest of the powder down the muzzle, follow that with the ball, and ram the paper down on top of them to hold them in place.

A rifleman would also sometimes use the musket drill, if required to fire rapidly, typically at close quarters.

You can read the various drills in the 1812 Handbook for Riflemen. Drilling to make loading automatic for the soldiers was very important, because if the soldier was excited , confused or distracted a mistake in loading ( like running the ball down the barrel before pouring in the powder) could disable his musket, until someone ( like the sergeant) could extract it with a ball puller, a screw on the end of a ramrod.

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Assuming that by 'musket' we refer to any muzzle-loading firearm commonly used in large formations, including light arquebuses from last quarter of 15th century and early 19th century rifles, we can safely say that the musketeers generally used many different tools facilitating loading process.

The most common of them were cartridges, already mentioned by /u/Bodark43. Their first recorded use in Europe is attributed to the Polish King Stephen Bathory (in documents from 1576 detailing armament and training of the volunteer infantry), what gives an assumption that he might have introduced this practice after witnessing it in his native Transylvania (what would mean that the first formation using it on a larger scale was Hungarian infantry in the second half of 16th century. This practice quickly became commonplace across Europe.

Earliest cartridges were simply pre-measured portions of gunpowder encased in the paper sleeve with twisted ends. Shooter had to rip or untwist one end, pour the powder, use the paper as wadding, then load a bullet from a separate pouch. Given that paper was not that cheap in the discussed period, and was not additionally protected from moisture, a popular alternative was a bandoleer (like this one: http://www.engerisser.de/Bewaffnung/weapons/Bandolier.html) with wooden flasks containing powder charges. These were much sturdier and more waterproof. They also give a good insight into the actual use of firearms during a battle, as charges carried by a single shooter was considered enough for a single encounter and most common bandoleers have between 8 and 14 of them. This strongly suggests that shooting was far from hectic, giving shooters plenty of time to load, aim and fire. On the other hand, Błażej Lipowski in his 'Infantry exercise or foot warfare' writes as follows:

Powder pouch needs to hold at least two pound of powder, and have three flasks or wooden capped cartridges (as worn with bandoleers) to fill separate charges, as it is more handy to fill flasks from the powder pouch beforehand (to load the musket faster should sudden need arise) that to scoop the powder by hand [...] Musketeer reporting for duty needs to have thirty bullets in a pouch and fifteen fathoms of burning match at the belt, as no time may find to get the match when the duty gets longer and this can sometime get carried over to the forthcoming day or when forced march gives no time to supply [...].

This means that thirty bullets and enough powder for thirty two charges (on average, early muskets used amount of black powder similar to the mass of the bullet, usually around 25 grams or 0,9 ounce, while Polish pound was roughly equal to 410 grams or 14.5 ounce) what was considered more than enough for two days of combat while three pre-measured charges seemed to be an adequate number facilitating fast shooting.

On the other hand, there are many surviving specimens of measuring devices, often incorporated into other tools. The most common would be the powder flask with a cap doubling as a simple measuring device or a separate metal sleeve carried as a separate item (like this one: https://commons.wikimedia.org/wiki/File:Powder_Measure_Ottoman_17_century.jpg). As soon as late 16th century, a powder flasks with double-action measuring spouts appear. These had metal diaphragm at the base of the spout and a cap on top of it. To measure a dose of powder, shooter had to turn turn the flask spout down, engage the diaphragm to separate the spout from the rest of the flask and then open the cap pouring the measured dose into the barrel. Later models had even adjustable telescopic spots to measure a specific amount of powder. Some shooters were using measures almost identical to one you have shown as an example, sometimes incorporated into a wheelock spanners, as evidenced here: http://www.ambroseantiques.com/hornsflasks/spann.htm or as a separate tool (https://commons.wikimedia.org/wiki/File:Blackpowder_Measure_17_century.jpg). Given their dimensions, it is safe to assume they were used for pistols rather than muskets.