By cycle, do you mean on the Particle logs, they keep saying they're online and then online, every 10 or so seconds? If so, to get them programmable now... try leaving one (or more if you want) powered up for up to 10 minutes, and see if it has stopped. If it has, you should be able to upload a new program to them. Make sure you have updated your board support package on the Arduino IDE (Tools -> Boards -> Board Manager) - I believe 1.0.5 is the latest. There appears to be an issue introduced between 1.0.2-1.0.4 which caused the Oak to keep cycling for several minutes, before finally entering a usable state.
If this fixes the problem, just be aware that config/safe mode is NOT updated when you upload a new program, so if you use config mode for some reason, it will suffer from the same problem. Best solution I personally have found for that is to simply push the new firmware via serial, using the
Serial Update instructions from the Wiki. Others have use the OakRestore instructions, but that then mean you still need to update the Oak like you did when you first got it, so I just skip that and push the latest firmware directly on. You'll need to make sure you disconnect & reconnect the power after it's finished, as the Oak usually doesn’t reboot properly.
Yes, that adapter should be fine, as it has the 3.3v jumper. Unless you need it right this minute, and have a local Jaycar store/reseller you can drop by, you can get a
module like this one from ebay for 1/10th of the price... it will just take 2-3 weeks for it to come via the post! :-(