Air conditioner light was blinking on and off and not getting very cold?

The air conditioner light flashing indicates there's a problem detected. It can be an electrical problem or low freon (usually). If the air conditioning system has a leak that means air has gotten into the system and adding Freon doesn't always correct the issue because the air in the system needs to be removed with an A/C machine. If you visually look at all the air condition parts under the hood to look for residue on the hoses, compressor, condenser and air condition ports. There shouldn't be any residue on these parts around seals or hoses.
If you do see residue then that is a clue for a leak and those parts will need to be replaced as the freon will leak out again after removing the air from the system and recharging. Recovering all the freon on the system will determine how much freon was in the system and give an idea that the system has a leak also.

From your description it doesn't sound like it's an electrical fault as it sounds like everything is working electronically

Let us know what you find or if we can give you more direction.

Most likely it's because there is air in the system already taking up space and not the freon only. The system will pump air along with the freon, but you won't get cooling out of it.

There could be something electrical wrong like the switch stopped working however, from what you've described it doesn't seem to be that way. I'm leaning more towards the freon being low and not electrical.

It sounds like you have too much refrigerant in the system, let's confirm by connecting a set of gauges then turn the system on to see what the readings are. Please go over this video to see what I am talking about:

https://youtu.be/4EqdrBVb0sY?si=A14_LKx7dF22txDh

Also, here is a guide that you can go over which should help as well:

https://www.2carpros.com/articles/car-air-conditioner-not-working-or-is-weak

Please go over these guides and get back to us.