For the exact effect you want, you can word the emblem as follows:
At the beginning of each upkeep, if this emblem has no Quickening counter on it, put a Quickening counter on it.
As long as this emblem has a Quickening counter on it, you may cast spells as though they had flash.
If you would cast a spell without a Quickening counter on it, ...
This is tricky, and may not be doable with the exact effect want.
One issue is that if you look at the Oracle text of Erayo's Essence, it is a triggered ability:
Whenever an opponent casts their first spell each turn, counter that spell.
A triggered ability will not work for casting a spell as though it had flash though, because if it triggered on ...
I don't know of an example to use for precedent, but I think this would work:
You get an emblem with "You can cast spells as though they have flash as long as you have cast fewer spells this turn than the number of copies of this emblem you have."
It's a little awkward, but it almost1 does what you want:
You get an emblem with "If you would cast a spell without flash, instead cast that spell, it gains flash, and this emblem loses all abilities until end of turn."
To cast a spell you have to follow a series of steps as described in rule 601.2. Our ability creates a replacement effect (by 614.1a) so ...
I think you could make this work by having an emblem that gets a depletion counter at the beginning of each turn if they do not already have one. Then you would word the emblem something like Decree of Silence, except make it explicitly say target so that the trigger can fizzle when one of the emblems counters a spell, the wording for this would be something ...