There are two main areas this change would impact: XP gains, and roleplay.
The bonds system gives, at most, 1 XP to a character per session. In practice, this is probably less, as there are likely to be sessions where a character doesn't change their bond with anyone.
With flags, it seems fairly likely that you can do it most sessions. If you don't have a maximum XP from different flags per session, you might accelerate faster. The website you linked does offer the possibility of removing XP gain from failed rolls if you're giving away more XP.
However, moving gains away from failed rolls may help keep XP gains more level across a group, and it doesn't encourage rolling all the time! That said, I don't feel like XP and levels are hugely important after you're around level 6 or so.
One thing about bonds is that they help you take a moment to explore your character's relationship with other characters. If you think about how your character feels, then your actions and decisions will be within that context, rather than whatever's convenient. There's a degree of immersion into your character's experiences that bonds can help, which flags don't encourage. These are explored somewhat in this question.
As the article mentions, flags are designed for a changing cast, where bonds may not make sense. Instead of colouring your interaction with a particular character, flags instruct others how to interact with you, to give you an opportunity to play out a defining part of your character. Depending on the flexibility of the flag, or how you envision your character, they may be ideal.
On the other hand, flags may also end up being more gimmicky. If players are just pushing your button once a session to give you XP, it becomes throwaway or artificial and may detract from the roleplay. Or it may limit your character, simply acting the same way each session, instead of pushing you to think about how your character's perception is changing.
I worry that it might be easy to write flags that contain your character's change and growth, rather than explore it. However, bonds can also be hard to write in a way that's actionable. I expect that, as with bonds, given a few tries, one would get better at writing flags that give you the opportunity to express your character in different ways.
That said, I think bonds are really useful as a concept, even if they're not mechanically incentivised with XP. If you're trying out flags, I'd still have people choose and review bonds between sessions.