Magento 2 Can't get the sales rules conditions in my ui form submit

You need to make your custom Conditions.php and just replace $formName argument of addTabToForm function with your form name.

you are using Magento core file and it's adding the selected value of conditions section in sales_rule_form form

Updated code :

eg.

    function addTabToForm($model, $fieldsetId = 'conditions_fieldset', $formName = 'example_form'){... }

Conditions.php

namespace Namespace\Example\Block\Adminhtml\Example\Edit\Tab;

use Magento\Framework\App\ObjectManager;

class Conditions extends \Magento\Backend\Block\Widget\Form\Generic 
{
    /**
     * Core registry
     *
     * @var \Magento\Backend\Block\Widget\Form\Renderer\Fieldset
     */
    protected $_rendererFieldset;

    /**
     * @var \Magento\Rule\Block\Conditions
     */
    protected $_conditions;

    /**
     * @var string
     */
    protected $_nameInLayout = 'conditions_serialized';

    /**
     * @var \Magento\SalesRule\Model\RuleFactory
     */
    private $ruleFactory;

    /**
     * Initialize dependencies.
     *
     * @param \Magento\Backend\Block\Template\Context $context
     * @param \Magento\Framework\Registry $registry
     * @param \Magento\Framework\Data\FormFactory $formFactory
     * @param \Magento\Rule\Block\Conditions $conditions
     * @param \Magento\Backend\Block\Widget\Form\Renderer\Fieldset $rendererFieldset
     * @param array $data
     */
    public function __construct(
        \Magento\Backend\Block\Template\Context $context,
        \Magento\Framework\Registry $registry,
        \Magento\Framework\Data\FormFactory $formFactory,
        \Magento\Rule\Block\Conditions $conditions,
        \Magento\Backend\Block\Widget\Form\Renderer\Fieldset $rendererFieldset,
        array $data = []
    ) {
        $this->_rendererFieldset = $rendererFieldset;
        $this->_conditions = $conditions;
        parent::__construct($context, $registry, $formFactory, $data);
    }

    /**
     * The getter function to get the new RuleFactory dependency
     *
     * @return \Magento\SalesRule\Model\RuleFactory
     *
     * @deprecated
     */
    private function getRuleFactory()
    {
        if ($this->ruleFactory === null) {
            $this->ruleFactory = ObjectManager::getInstance()->get('Magento\SalesRule\Model\RuleFactory');
        }
        return $this->ruleFactory;
    }

    /**
     * {@inheritdoc}
     * @codeCoverageIgnore
     */
    public function getTabClass()
    {
        return null;
    }

    /**
     * {@inheritdoc}
     * @codeCoverageIgnore
     */
    public function getTabUrl()
    {
        return null;
    }

    /**
     * {@inheritdoc}
     * @codeCoverageIgnore
     */
    public function isAjaxLoaded()
    {
        return false;
    }

    /**
     * {@inheritdoc}
     * @codeCoverageIgnore
     */
    public function getTabLabel()
    {
        return __('Conditions');
    }

    /**
     * {@inheritdoc}
     * @codeCoverageIgnore
     */
    public function getTabTitle()
    {
        return __('Conditions');
    }

    /**
     * {@inheritdoc}
     * @codeCoverageIgnore
     */
    public function canShowTab()
    {
        return true;
    }

    /**
     * {@inheritdoc}
     * @codeCoverageIgnore
     */
    public function isHidden()
    {
        return false;
    }

    /**
     * Prepare form before rendering HTML
     *
     * @return $this
     */
    protected function _prepareForm()
    {
        $model = $this->_coreRegistry->registry(\Magento\SalesRule\Model\RegistryConstants::CURRENT_SALES_RULE);
        $form = $this->addTabToForm($model);
        $this->setForm($form);

        return parent::_prepareForm();
    }

    /**
     * Handles addition of conditions tab to supplied form.
     *
     * @param \Magento\SalesRule\Model\Rule $model
     * @param string $fieldsetId
     * @param string $formName
     * @return \Magento\Framework\Data\Form
     * @throws \Magento\Framework\Exception\LocalizedException
     */
    protected function addTabToForm($model, $fieldsetId = 'conditions_serialized', $formName = 'productex_form')
    {
        if (!$model) {
            $id = $this->getRequest()->getParam('id');
            $model = $this->getRuleFactory()->create();
            $model->load($id);
        }
        $conditionsFieldSetId = $model->getConditionsFieldSetId($formName);
        $newChildUrl = $this->getUrl(
            'sales_rule/promo_quote/newConditionHtml/form/' . $conditionsFieldSetId,
            ['form_namespace' => $formName]
        );

        /** @var \Magento\Framework\Data\Form $form */
        $form = $this->_formFactory->create();
        $form->setHtmlIdPrefix('rule_');
        $renderer = $this->_rendererFieldset->setTemplate(
            'Magento_CatalogRule::promo/fieldset.phtml'
        )->setNewChildUrl(
            $newChildUrl
        )->setFieldSetId(
            $conditionsFieldSetId
        );

        $fieldset = $form->addFieldset(
            $fieldsetId,
            [
                'legend' => __(
                    'Apply the rule only if the following conditions are met (leave blank for all products).'
                )
            ]
        )->setRenderer(
            $renderer
        );
        $fieldset->addField(
            'conditions',
            'text',
            [
                'name'           => 'conditions',
                'label'          => __('Conditions'),
                'title'          => __('Conditions'),
                'required'       => true,
                'data-form-part' => $formName
            ]
        )->setRule(
            $model
        )->setRenderer(
            $this->_conditions
        );

        $form->setValues($model->getData());
        $this->setConditionFormName($model->getConditions(), $formName);
        return $form;
    }

    /**
     * Handles addition of form name to condition and its conditions.
     *
     * @param \Magento\Rule\Model\Condition\AbstractCondition $conditions
     * @param string $formName
     * @return void
     */
    private function setConditionFormName(\Magento\Rule\Model\Condition\AbstractCondition $conditions, $formName)
    {
        $conditions->setFormName($formName);
        if ($conditions->getConditions() && is_array($conditions->getConditions())) {
            foreach ($conditions->getConditions() as $condition) {
                $this->setConditionFormName($condition, $formName);
            }
        }
    }
}