Marriages don't run on their own, they need constant care and work to keep them functioning properly. That being said, you're going to have up times and down times, and it sounds to me like you're possibly moving into the latter. (I don't think you're there yet.) It's easy to get so caught up in your lives apart, that you forget to pay attention to the time together. Or rather, it just gets easier to "leave it alone" and hope that it'll work itself out. Sometimes that can happen, but more often than not, it takes both partners to put effort into re-strengthening a marriage. (This has been my experience anyway- been married over 10 years.)
As far as the flirting thing goes, well it's not going to be exactly like it was in the beginning, because back then it was new territory. If you're having a disconnect right now, I would suggest to start small with little touches or words during the day that bring that spark back. Smack him on the behind as you walk by, wink at him, scratch his back for a minute for no reason. The little things eventually add up, and thinking it sounds fun, he might start playing along. It might take effort at first to start these kinds of things, but it could snowball into something better and by then it won't take any work at all- it'll just happen on its own. (The little touches etc. is also a great thing to start with if the problem deep down is sex related (or lack thereof).
It's good of him to want you to continue school. That means that he cares about your future. His complaint about you needing to spend more time together despite that, sounds like he's just as lost as you in in knowing what to do next. Doing the dishes together is a small, but good thing to do together, because it shows that you're working as a team- partners. Talking is the best thing I think, because it has more of a lasting effect than any activity. You could take a walk together outside and discuss your day, or talk about your plans over breakfast. Make dates with each other, because since you have individual lives, it's not automatic that every time you're available, he will be also. You need to plan to be together.
Like I said in the beginning of my post, I don't think you're in a "down time," but you could be if things slide further. After a while of being distant, feelings could begin to turn bitter and it will take a lot more work to come back from that. It's good that both of you are aware of the problem, and even if he's not as vocal about fixing it as you are, him bringing it up is a sign that he's willing to work on it. The very best thing to do is talk to each other, because no one is a mind reader. You should do so in a relaxed, open minded way. Don't demand answers, patiently ask for solutions. Be a good listener, don't interrupt each other so that you are sure to get everything out.
Saving 