There are a few things you can accomplish with Inkjet:
-Ink turf
-Make pathways for your team
-Kill enemies
-Break Rainmaker capsule
-Completely destroy anyone on the tower
-Diversion
-Reviving Teammates (Salmon Run)
How you use some of these tactics are self explanatory, but the three things I want to highlight is enemy killing, diversion, and path making. When you're trying to kill enemies, aim for where they're going *NOT* where they are. This piece of advice is Especially useful in Inkjet 1v1's.
Diversions are a tad bit more situational (and harder to pull off on more skilled players), but in Turf War/Rainmaker using Inkjet to distract your opponents so your team can land a victory is a valid strategy. Just make sure to fly away from where your team is at, and keep in mind this strategy won't work too well if there are Chargers/Sloshers/Squelchers on the opponents team.
Making pathways for your team is especially useful in Rainmaker (Or any other mode if you need to make a path. It's just way more useful in Rainmaker). If you Ink up a shortcut with Inkjet (and let your team know your doing this), you could land a pretty easy victory. This tactic can also be used for Salmon Run with great results.
This Special takes a bit of getting used to, but once you do; you'll pose a huge threat :)