Grind the carrots, tomatoes, and red chili powder to a smooth purée. Mix the flour, oil, and salt. Add the ground purée and knead to a smooth dough. Cover and set aside for an hour.
Grind the spinach, sugar, and green chili to a smooth paste sprinkling about two tablespoons of water. Mix flour, oil, and salt in a bowl. Add the ground spinach purée to the flour mixture and knead to a smooth dough. Cover and set aside for an hour.
Add flour, salt, oil to a bowl and mix. Sprinkle water and knead to a smooth dough. Cover and set aside for an hour.
Divide the dough into 25-30 equal pieces (in total), cover, and rest for 30 minutes to an hour.
Take one dough of each color (keeping the remaining covered), and place them side by side according to the tricolor standard. Press gently with hands and attach the dough. Gently roll into a rectangle shape dusting with flour as necessary. Repeat with the remaining dough. At this stage, the poori is can be cut into circle or can be kept as such
Heat oil over medium heat. When hot carefully drop each Luchi into oil. Gently press with a strainer ladle puffing the Luchi. Flip and fry the other side for a minute. Remove from oil and drain the excess oil. Repeat with the remaining flattened dough.
Serve with any curry.