Acquiring an antimagic field
The typical wizard must be level 11 to cast the 6th-level spell antimagic field, but once he can, the rogue could commission from him magic items. It's even possible that when the wizard hits level 11, the wizard takes the feat Craft Staff, and a staff is the easiest and cheapest way for the rogue to use the skill Use Magic Device to cast consistently the spell antimagic field, but the rogue must find means to recharge the staff when it's depleted. The cost to create a staff of antimagic field is 26,700 gp, which includes the 300 gp for the masterwork staff. (The base price for a scroll of antimagic field (6th-level arcane spell at caster level 11) is 1,650 gp if the rogue only wants to use the spell once.)
Without many other items that create an effect like the spell antimagic field, the equalizer shield (120,830 gp; 23 lbs.) appears to be the item to use when ballparking prices for similar items that create an effect like the spell antimagic field. The fact that without the equalizer shield's ability to create an antimagic field once per day the equalizer shield is just a +1 mithral tower shield means the game puts the price of the ability to generate an antimagic field on command once per day at upwards of 100,000 gp.
Adjudicating an antimagic field
The spell antimagic field's spell level belies its vast power; it's one of the most powerful and difficult to manage effects in the game. It allows the defeat of many foes the PCs would've otherwise found invincible, and it allows the weak foes to defeat the PCs. It's a nuclear weapon that sends all users back to the Stone Age time of No Magic, and that's scary. Even creatures who plan around the spell can be hurt by the spell's unpredictability; the nature of PCs' adventures rarely make adventuring without magic a good idea.
To that end, I agree with Ciacciu's answer: experiment. Start with a scroll or two and see how it changes your game, and remember to let the foes do the same.
Flying does not equal Mounted
Being mounted is very different than flying. The Lance specifically requires you to be mounted in order to avoid the penalty for one-handed use. Mounts are covered in the PHB (page 155), and nowhere does it state that flying/swimming/walking yourself would ever qualify as a mount.
In order to be able to wield a Lance one-handed without disadvantage, you would need a legitimate mount that you are actively riding.
Best Answer
Yes, Aasimar can use this ability in an antimagic field
Only magic and magical effects are affected by an anti-magic field as indicated in the description of the spell:
Sage Advice gives us tests for determining if something is considered magical. I will go through and apply these tests to the Radiant Soul ability.
Nope.
It is not a spell and no spell is mentioned in its description. See this Q&A for a description of how to tell if something is a spell.
It isn't a spell or an attack so no.
It uses no spell slots.
Nowhere in the description does it say it is magical.
The Aasimar ability Radiant Soul passes none of these tests and is thus not magical. Since it is not magical it is not affected by antimagic field.