I just started this myself recently. I had one license already to start with (IL). I submitted my information and requested documents to be sent to FCVS at the end of June, and applied to five states (mix of UA and state applications). If you pick a state like Wisconsin, that doesn't require fingerprinting/background check, or any other add on tests or CME requirements, and get all of your documentation in quickly yourself, you could get a license in a month. WI issued my license a day after they received my FCVS file (1 month from when I started the FCVS and WI applications), so that appeared to be the rate limiting factor. Another rate limiting factor is if you already have a license in another state. Waiting for that state to send proof of your license by mail can take time, but call and check - I actually found out that if I fed-exed my request with a self-stamped return fed-ex envelope, IL would process the request in 10 days instead of 6 weeks. It did not say that anywhere on the web site. Or you could be lucky to have your current license(s) in a state that transmits it electronically. I also got my Indiana license just one week after my WI license, even with sending them my fingerprints for the background check. Funny how the states with the inexpensive licenses are so much faster....
I also applied to AZ, CA and TX at the same time. All require fingerprinting; yet another duplicitous step. For TX, everything is done except the jurisprudence exam, but I was told that if I get it done this month, I should probably expect my license by November. That would be 4-5 months. AZ has nothing extra (other than the fact that they basically want an original copy of your passport as proof of citizenship - funny, that), and said I should expect it by October (3 months). No idea what CA is up to. I had some delay because I had to wait for CA to mail me their own stamped generic FBI finger print cards. I also just half-heartedly applied to FL a week ago, but am getting tired of repeating all of the same steps. The licenses are also about $1000 each. Info I wish I'd realized: some states give a big discount if you apply while you're a resident (CA), while others only give a discount if it is approved while you are a resident (FL). Also a good idea to apply all at once to as many states as you think you'll want to get licenses in before you obtain a bunch of licenses that you'll have to send to every other state, and before you have employment history that needs to be verified. Ideally, I should have done this all six months prior to finishing residency.
I agree that this process is absolutely ridiculous, even with FCVS or the UA. The fact that there is no one repository or national verification is unbelievable. FCVS is a step in the right direction, but there are still so many other pieces that you have to send to each and every state. If FCVS verified state licenses as well, now THAT would be fantastic. And after having to prove to several states that yes, I am a citizen, yes I went to medical school, residency, have no lawsuits against me, etc., etc., etc., and THEN after getting the license, having to submit all of the same information again to a hospital board and start over again..... And it really does seem like a joke that you have to get separate federal DEA numbers (>$700) for each individual state (or playing some games (suggested to me by the DEA itself) with address switching between state locums gigs).... Wait, isn't that supposed to be federal? As in national? Apparently "it's been years" since you could use one DEA number in several states.
Bottom line, is that you should probably just figure out geographically where you want to do locums, figure out where the best pay is (if that's your primary motivator), or get an agent who will pay for and do all of this for you. Alternatively, if there's a specific hospital or group you want to work for, they may even pay for it if you're negotiating with them directly without a locums agent.
Also, beware that if you "have prior contact" with one or two of the big locums agencies, they call dibs on you nationally. I think one of them even claimed prior contact with me solely by my having swiped my badge at their booth at ACEP to pick up their brochure and get a phone charger. Because I certainly had never emailed/called/talked to them. How their having your name/email in their database is some sort of binding contract in the locums world is beyond me. I have another friend who did talk to one of them (but did not send their CV or discuss specifics), and they were unable to be placed at a few hospitals by other locums agencies due to that "prior contact." Perhaps we need another post to collect all of the web sites that have independent/PRN opportunities on them for those applying for their own licenses and trying to avoid locums groups. Or better yet, a post to call out the locums groups and try to keep them honest by shining some light on these practices. Sorry for the accidental derailment. But it's stuff I wish I'd known before starting this process.