I will be traveling from Leeds UK to Amsterdam via KLM. I will have one checked bag. I will then be traveling from AMS to the US on a different ticket on United Airlines, so I will have to clear immigration and retrieve the checked bag and then check in again for the second flight. There is a three-hour gap between landing and takeoff of the two flights. Is that enough time?
No one knows. There are no guarantees.
If all goes "normally" this will probably work. If there are any significant problems (delayed flight, baggage issues, long line at immigration, bad weather, etc.) then you won't make it.
By booking two tickets, you assume the full risk of missing the connection and it's up to you how much wait time you want to bake in as "insurance". That should be a function of the risk of delay and the consequences of the delay, i.e how much money is at stake and how do you value extra wait time vs. cash or schedule risk.
The beauty of a single ticket is that the airlines assume this risk. They can easily do this, since they have lots of statistical data to determine what "minimum connection times" make sense for them.
Personally, I would budget at least 4 hours for a connection like this.