How many amps should my aux battery be charging at

Your max charging rate of your battery is dependent on its Amp hour rating , its is usually round 1% of your CCA, so 620CCA is 6Amps. Note that different chemistries of batteries have different voltages for charging (Lead or Calcium lead (Low maintenance)) or gel based batteries .If your using the Amp Hour approach it is generally 30% of its Amp hour rating

For almost every alternator after 2000, the alternator has a built-in regulator, you can't change the voltage manually.

The voltage is usually to be cut-off at 14V ±1V.

If you still concerned about getting overvoltage to your battery, you can add an old voltage regulator for your battery. Like this:

Or add a digital one.

For current related is what binaryops20 said, it's calculated from what type of your battery, how many Ah (Amp hour), or how many CCA (Cold Cranking Amp).

For Ah rating, the minimum charge is 10% of max Ah. You can charge your battery up to 50% from Ah rating (wet battery lead-acid) but you will degrade your battery faster than charging 10% from Ah rating.

For CCA rating is usually the minimum charge is 1/6 of the CCA rating. but all depending on your battery type.

you can find in here for further information:

• Powerstream.com
• batteruniversity.com

Most alternators are usually regulated to about 5 amp/hours in car applications. Assuming your batteries are identical in characteristics and wired in parallel. The charge current would be split equally between the two batteries. As a result it would take twice as long to charge as it would with a single battery.

If you want to charge 2 batteries yet use then for separate purposes like one for starting the vehicle and the other one running other stuff you can get a device called a battery isolator at places that sell parts for RV's

Amp/hour ratings refer to the safe charge and discharge current for 1 hour intervals.

The CCA rating is the discharge load in amps of a fully charged battery at -18C /0F for 30 seconds while maintaing a terminal voltage of 1.2V or higher per cell .

If you’re charging from your vehicle‘s alternator or from a charger that’s designed for lead-acid then you have nothing to worry about.

The "best" way to connect a second battery to your vehicle is to use a "caravan relay" or more properly named a "split charge relay".

these come in various types and some have an "over-ride" to enable the second battery to be used to start the vehicle if necessary.

Do a search on suitable sites or stores and you will find them.