Congrats on the promotion! so far I've only worked with 5 different flow TLs, each of them very different from the other. The most successful 2 of them had A) years of experience as flow TLs and B) been promoted from a flow TM. The two least successful were transferred from team leads in other departments (presentation and backroom team leads), and the other one is still fairly new, and from outside the company.
Things to DO would be complete openness and honesty with your team. If your STL and ETL are telling you things pertinent to a particular TM or to your whole team, you need to relay that information. I remember one time where we waited for months before our ETL-Log told us that we were zoning the entire store incorrectly as we pushed, causing half the team that got hired and trained in that time to learn how to do everything the wrong way.
Make sure to hold everyone accountable to the same standard. If your team perceives you as fair this will go a long way to winning their trust. If you let one person get away with pushing an aisle at 1 carton every two minutes and everybody else is pushing at the standard case per minute, they better damn well have a medical restriction.
Don't get too chatty with particular team members, and be cold to others, this will get noticed. The one time I've seen a team lead fired was when a flow tl let this disparity turn into a physical dispute. My first flow tl had been working with some of her tms for nearly a decade. Now, when most of the team was gone I would see her chatting them up, asking them about their personal life and the like, but when everybody else was around she treated them like everybody else.
Don't condescend to your TMs. I've never seen a flow team lead do this, but I've seen most of the ETLs (especially the young ones) do this. It may be tempting to talk down to your TMs, but remember they won't respect you if you don't respect them. You can only give instruction to your team by talking to them as equals, if you act superior to them they won't take you seriously.
Hope this helps!