Hopefully you don't plan for the conure to spend much time on the floor, so the biggest concern will be off-gassing.
(Allowing a small bird to walk around on the floor on a regular basis, is simply asking for a bad accident to occur. Added to that, with foam tiles, IF you encourage the bird to spend time on the floor, a conure will almost certainly get to work ripping up the foam.)
I don't know specifics with regard to specific foam flooring. That is, does it continue to off-gas, and for how long after installation, etc.
However, IF you do go ahead with this flooring, I have two big suggestions:
FIRST, and most important: Open all the Packaging and Remove all the packaging Far Away from the room where your birds will live. Preferably, OPEN the package OUTSide IF possible.
There can be a lot of "new carpet" / "new furniture/product" odor (aka fumes!) which seem to emanate from the item but Actually a large amount of those fumes are trapped in the Packaging. If you unwrap them inside the room, All that trapped off-gassing, will get into your room. If you can unwrap them outside, it will dissipate, and you will only need to wait for the actual, current off-gassing to air-out.
Second recommondation is just to make sure you do Allow Time for the flooring tiles to air out; some time, before putting them down; and, if possible, also some further time once the tiles are in, before putting the bird in the room.
An air filter can help with this. Really, it is advisable to invest in a good air filter anyway for your bird, if you are able.