The intent is to ensure your battery doesn't discharge enough to interrupt a flash in progress.
Rather than worry about a trickle charger or a jump pack's output I'd just connect a second car battery using a set of jumper cables (connected to the jump points under your bonnet). This could be done with a 'stand-alone' battery or a jump between two cars.

 

That's what I was thinking. I didn't know if it was totally insane, or totally brilliant. I'm assuming I should keep the donor car engine running...

 

I'm assuming I should keep the donor car engine running...

I doubt you'd run down two car batteries during a flash but keeping the 'donor' car running couldn't hurt.

 

Better safe than sorry. It's probably a liability thing on their end.

 

Donor car? Not sure what is meant there unless you mean using a second car connected to the first to provide battery charging?

Realistically any 4A+ charger is probably perfectly fine, so long as your battery:
1. Is fully charged to begin with. To ensure this, charge it fully before beginning, to where the charger says full or green or whatever.
2. Is in good general condition to begin with. In this case load test your battery after charging and be sure it's at least showing 70% SOH.

After that you should be perfectly fine to flash it just on the 4-5A charger, no problems. If you have an ailing battery (50% SOH or less) or cannot achieve a full charge on it (like charger errors out), then in that case I'd def. replace the battery first.

"Charging" from another car for that long is not really ideal or recommended TBH. Probably nothing bad will happen (and I'm guessing you've already done so), but it's typically not a good idea to keep booster cables going across two cars for extended periods.