This is a state of mind rather. Why not the trait? Because everyone can experience it, moreover, does it, depending on the proportions between the difficulty situation (task) and the necessary skills one developed. It works along with the Yerkes-Dodson laws of human motivation. Our skills and predispositions either.
By the way: I appreciate Csikszentmihalyi's contribution to the understanding the flow experience very much, but Yerkes and Dodson were much earlier.
Both. As with more conventional emotions (e.g., positive affect), people may have trait-like dispositional tendencies to experience flow. A recent longitudinal study of flow during musical performance rehearsal presents evidence that most variance in self-reported flow experience occurs at the state level within individuals, but not all (Fullagar, Knight, & Sovern, 2013; linked below). I.e., there are also apparently some stable differences in the propensity for flow experience. A nice discussion of this exact issue begins at the bottom of page 251 and carries through to the bottom half of the next page. It's a cool study; check it out!
I do not recall the exact reference but Sue Jackson and Bob Eklund have created and validated questionnaires to measure flow as a state and flow as a trait.
Flow is typically considered a state but, as mentioned above by Nick, there are individual predispositions to seek challenge and experience flow. Csikszentmihalyi refered to an autotelic personality. You might want to check up this chapter:
Right, any state of mind determines at least one 'individual predisposition'. this does not mean that this determinant is simultaneously the determined. It does not make sense. It is like baron Muenchhausen, who pulled out himself by his own hair from the swamp!
Nicola Baumann proposed the intrinsic part of the achievement motive à la McClelland as a disposition for flow states. You might want to check out her publications: https://www.uni-trier.de/index.php?id=5996&L=2
This is the good answer. However, I suspect that not this single disposition accounts for the flow experience, nor the flow is the single outcome of the intrinsic part of achievement motive.