That does not work
The hand crossbow states:
You can shoot, but not load, a hand crossbow with one hand at no penalty. You can shoot a hand crossbow with each hand, but you take a penalty on attack rolls as if attacking with two light weapons.
So, with a hand crossbow in each hand, no matter if you have Rapid Reload or not, you cannot reload either of the two crossbows as you have no free hand. The only benefit the second crossbow could give you if it is loaded is a single additional attack before you need to drop it so you can reload your other crossbow.
A 20th level Rogue has a base attack bonus sequence of 3 attacks for a full attack, and epic levels do not change that, they just increase the to-hit bonus. So they could make the attack with the off-hand hand crossbow, drop it, and do another 3 attacks with their main-hand hand crossbow, for a grand total of four attacks.
Rapid Reload does not free you from needing a free hand to reload. It states:
The time required for you to reload your chosen type of crossbow is reduced to a free action (for a hand or light crossbow) [...]. Reloading a crossbow still provokes an attack of opportunity.
If you have selected this feat for hand crossbow or light crossbow, you may fire that weapon as many times in a full attack action as you could attack if you were using a bow.
Normal two-weapon fighting gives you one additional attack:
If you wield a second weapon in your off hand, you can get one extra attack per round with that weapon.
The two weapon fighting feat does not grant you any additional attacks, it just reduces the attack penalites. Improved two weapon fighting and Greater two weapon fighting would give you a second and third attack with your off-hand weapon, but as you cannot reload it, those will do you no good.
How to get to more attacks?
If the character also had the Quick Draw feat, which you say they do not have, they might be able to draw additional hand crossbows as a free action, and if those were already loaded and cocked before the fight, could use the second and third attack with the off-hand weapon by dropping the first hand crossbow, quick drawing the second, dropping that and quick drawing the third, and after dropping that one, moving on to your normal attacks with Rapid Reload. That would bring the total attacks to six, for 7 free actions overall used. Still not 8 attacks, though.
@wannabe-warlock suggest alter self, to get an extra hand to help with loading. If that will work will depend how your DM rules on the clause "A body with extra limbs does not allow you to make more attacks (or more advantageous two-weapon attacks) than normal". On a strict read, you cannot use them to make more attacks, no matter how, but if your DM agrees to allow them to reload the weapon, as long as they are not used to attack themselves, it could be yet another way around the reload limitations.
A glove of storing (thanks to @mr-tumnus for the suggestion) or glove of the master strategist (from Ghostwalk) could also help to store a hand crossbow you do not need as a free action. If you had two of those, you could free up the hand you currently are not firing with for loading the other, although on a strict applciation of the rules, even though the glove is named singular, you only can have one item in the glove slot. A kimono of storing (20,000 gp, Oriental Adventures) has two sleeves that work the same way, and gets around that.
@kryan dug up this list of methods that, in addition to such shenanigans, includes:
- Dragon Tail (Races of the Dragon, needs draconic bloodline and must be taken at 1st level) + Prehensile Tail (Serpent Kingdoms) feats
- Girallon's Blessing spell (Spell Compendium)+ Permanency spell
- Mighty Arms graft (1,000 gp, Faiths of Eberron, if you do not need to replace your own arms - so unclear if it really works)
- Collar of Perpetual Attendance for Unseen Servant (2,000 gp)
- Phylactery of Change (11,200 gp, Arms & Equimpment Guide)
- Spare Hand (12,000 gp, Magic Item Compendium).
- Fleshshifter Armor (13,160 gp, Book of Vile Darkness)
- Taloned Arm (34, 000 gp, Races of the Dragon)
- Arms of the Naga (56,000 gp, Savage Species)
As @joedragons points out, you also could use a magic item that gives you haste, like boots of speed, which would add one more attack to your full attack action, bringing you to 7.